Catch those negatives

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

cappucher

93 posts

cappucher

#1 h Nov 7, 2024, 5:08 PM • 1 Y

Y by IanJung

How many ordered pairs of integers $(m, n)$ satisfy $\sqrt{n^2 - 49} = m$ ?

$\textbf{(A) }1 \qquad \textbf{(B) }2 \qquad \textbf{(C) }3 \qquad \textbf{(D) }4 \qquad \textbf{(E) } \text{Infinitely many} \qquad$

This post has been edited 3 times. Last edited by cappucher, Nov 8, 2024, 4:46 AM

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

mithu542

1570 posts

mithu542

#2 h Nov 7, 2024, 5:10 PM

Y by

I got $(D)$ . Just squared and used difference of squares

I almost did 2 until I realized that negative solutions are allowed lol

This post has been edited 1 time. Last edited by mithu542, Nov 7, 2024, 5:10 PM

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Vivaandax

79 posts

Vivaandax

#3 h Nov 7, 2024, 5:11 PM • 3 Y

Y by IanJung, wangzrpi, Aaronjudgeisgoat

Maa really loved to troll people with the negatives on this test

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

xiaoya.peng

120 posts

xiaoya.peng

#4 h Nov 7, 2024, 5:11 PM

Y by

I got 2 because m can't be negative and the absolute value of n can't be less than 7 so that got rid of some solutions

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

mithu542

1570 posts

mithu542

#5 h Nov 7, 2024, 5:12 PM • 1 Y

Y by sadhase25

oh oops i forgot about that

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

MathRook7817

662 posts

MathRook7817

#6 h Nov 7, 2024, 5:12 PM

Y by

mithu542 wrote:

I got $(D)$ . Just squared and used difference of squares

I almost did 2 until I realized that negative solutions are allowed lol

bro same

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

LostDreams

144 posts

LostDreams

#7 h Nov 7, 2024, 5:16 PM

Y by

Square it and apply differences of squares and you notice that there are 4 possibilities when you bash which is (24, 25), (24, -25), (0, 7), and (0,-7)

Giving us the answer D

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Siddharthmaybe

106 posts

Siddharthmaybe

#9 h Nov 7, 2024, 5:20 PM

Y by

Lol people really thought they tricked the question but the question tricked them, m can't be -ve cuz its square root function

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Alex-131

5361 posts

Alex-131

#10 h Nov 7, 2024, 5:20 PM

Y by

I have no idea whether I did C or D, rip. I got the negative solutions, but I don't remember whether I put (0,-7) in. kms

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Siddharthmaybe

106 posts

Siddharthmaybe

#11 h Nov 7, 2024, 5:22 PM

Y by

Alex-131 wrote:

I have no idea whether I did C or D, rip. I got the negative solutions, but I don't remember whether I put (0,-7) in. kms

ya i just realized that too i don't remember that

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

stjwyl

1262 posts

stjwyl

#12 h Nov 7, 2024, 5:37 PM

Y by

wait so wats the answer

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

ostriches88

1528 posts

ostriches88

#13 h Nov 7, 2024, 5:39 PM

Y by

stjwyl wrote:

wait so wats the answer

D

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

ethanzhang1001

1060 posts

ethanzhang1001

#14 h Nov 7, 2024, 5:59 PM

Y by

Vivaandax wrote:

Maa really loved to troll people with the negatives on this test

they also should've put 8 as an answer choice in E instead because what if you accidentally set m negative

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

ElaineGu

388 posts

ElaineGu

#15 h Nov 7, 2024, 6:07 PM

Y by

7 24 25 makes it trivial lmao
25, -25, 7, -7 for n

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

wangzrpi

159 posts

wangzrpi

#16 h Nov 7, 2024, 6:30 PM

Y by

Factor by difference of squares and you see that there are 8
There are 4 extraneous
So I picked the largest one (4)

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

pingpongmerrily

3569 posts

pingpongmerrily

#17 h Nov 7, 2024, 6:32 PM

Y by

i put 3 bc i thought that square roots couldn't be negative or smtg

:noo:

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

golden_star_123

206 posts

golden_star_123

#18 h Nov 7, 2024, 7:01 PM

Y by

Nobody has put a full solution so here it is:

$\sqrt{n^2-49} = m \implies n^2 - m^2 = 49$ . We have a difference of squares, so $(n-m)(n+m) = 49$ .

If $(n-m)(n+m) = 7\cdot 7$ , we have $n=7, n=-7$ and $m=0$ . This gives two possibilities.

If $(n-m)(n+m) = 49\cdot 1$ , we have $n=25, m=-24$ . This doesn't work, however, as a square root is always positive.

If $(n-m)(n+m) = 1\cdot 49$ , we have $n=25, m=24$ . One possibility.

If $(n-m)(n+m) = -49\cdot -1$ , we have $n=-25, m=24$ . One possibility.

This adds up to a total of $\boxed{4}$ possibilities.

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

cyberhacker

401 posts

cyberhacker

#19 h Nov 7, 2024, 7:01 PM

Y by

bro i put 4 and changed to 2?? i was fenting

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

williamxiao

2510 posts

williamxiao

#20 h Nov 7, 2024, 7:08 PM

Y by

Why did I put 3 it’s literally a square problem so it has to be even

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

ElaineGu

388 posts

ElaineGu

#21 h Nov 7, 2024, 7:09 PM

Y by

williamxiao wrote:

Why did I put 3 it’s literally a square problem so it has to be even

which case did u forget

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

pingpongmerrily

3569 posts

pingpongmerrily

#22 h Nov 7, 2024, 7:18 PM

Y by

williamxiao wrote:

Why did I put 3 it’s literally a square problem so it has to be even

sameee :sob:

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

ChaitraliKA

1004 posts

ChaitraliKA

#23 h Nov 7, 2024, 8:31 PM

Y by

williamxiao wrote:

Why did I put 3 it’s literally a square problem so it has to be even

Unless if 0 had worked

Anyways, I got this question right in the wrong way :rotfl:

who cares honestly

This post has been edited 1 time. Last edited by ChaitraliKA, Nov 7, 2024, 9:34 PM

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

awzhang10

72 posts

awzhang10

#24 h Nov 7, 2024, 8:54 PM

Y by

i had brainrot during the test and put infinitely many LOL

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Akang11

36 posts

Akang11

#25 h Nov 7, 2024, 9:43 PM

Y by

Sillied on the negative roots, please send help :sob:

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

SkatingKitty

223 posts

SkatingKitty

#26 h Nov 7, 2024, 10:10 PM

Y by

I crashed out and I left it blank

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

goldenuni678

237 posts

goldenuni678

#27 h Nov 7, 2024, 10:47 PM

Y by

I got D, from squaring and then using difference of squares

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

SkatingKitty

223 posts

SkatingKitty

#28 h Nov 7, 2024, 11:07 PM

Y by

I forgot the formula tears

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

andrewcheng

525 posts

andrewcheng

#29 h Nov 7, 2024, 11:30 PM

Y by

I got C because I forgot -7,0

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

gicyuraok2

1059 posts

gicyuraok2

#30 h Nov 7, 2024, 11:48 PM

Y by

dang i probably would have sillied this one but anyway $0,\pm7$ and $\pm24,25$ fun stuff

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

smarty101

322 posts

smarty101

#31 h Nov 7, 2024, 11:53 PM

Y by

forgot about 7-24-25 triangles :wallbash:

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

BrighterFrog11

1116 posts

BrighterFrog11

#32 h Nov 8, 2024, 10:33 PM

Y by

aww man. I got this one wrong. I didn't think about 0 and +/- 7

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

lpieleanu

2913 posts

lpieleanu

#34 h Nov 8, 2024, 10:45 PM

Y by

Solution

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

jb2015007

1917 posts

jb2015007

#35 h Nov 9, 2024, 3:29 PM

Y by

lol I actually got this right in like 2 mins cuz I was being cautious

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

NS0004

186 posts

NS0004

#36 h Nov 9, 2024, 3:53 PM

Y by

How can m be negative because of the square root?

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

pingpongmerrily

3569 posts

pingpongmerrily

#37 h Nov 9, 2024, 3:58 PM

Y by

NS0004 wrote:

How can m be negative because of the square root?

this is what i thought during the test but think a little harder, there are still 4 cases without m being negative

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Serengeti22

1135 posts

Serengeti22

#38 h Nov 9, 2024, 4:02 PM

Y by

I but 2 , I didn’t realize the negatives. The answer is 4

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Challengees24

1098 posts

Challengees24

#39 h Nov 9, 2024, 5:06 PM

Y by

Did anyone else make a graph lol

n^2+m^2=49, circle with 4 roots

(0,7),(7,0),(-7,0),(0,-7)

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

golden_star_123

206 posts

golden_star_123

#40 h Nov 9, 2024, 5:12 PM

Y by

Your approach doesn't work because m can't be negative.

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Challengees24

1098 posts

Challengees24

#41 h Nov 9, 2024, 5:32 PM

Y by

oml lmho i did it wrong way and still got the answer write

daym

This post has been edited 1 time. Last edited by Challengees24, Nov 9, 2024, 5:33 PM

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Challengees24

1098 posts

Challengees24

#42 h Nov 9, 2024, 5:34 PM • 1 Y

Y by PikaPika999

I just realized it should have been $n^2-m^2=49$

heyyy maybe this test wasnt so bad lol(joke kinda sorta, cuz it wasnt that bad)

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Apple_maths60

24 posts

Apple_maths60

#43 h Apr 4, 2025, 4:19 PM • 1 Y

Y by PikaPika999

I don't think (7,0)or (-7,0) would be a solution because if we put zero in the main equation we get √(-49)=m×m .
But √(-49) is not possible
So the answer must be 2
(25,-24)&(25,24)

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

NS0004

186 posts

NS0004

#44 h Apr 5, 2025, 4:05 PM • 1 Y

Y by PikaPika999

Bruh amc said the answer was 4....

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

AbhayAttarde01

1484 posts

AbhayAttarde01

#45 h Apr 5, 2025, 5:20 PM • 1 Y

Y by PikaPika999

Apple_maths60 wrote:

I don't think (7,0)or (-7,0) would be a solution because if we put zero in the main equation we get √(-49)=m×m .
But √(-49) is not possible
So the answer must be 2
(25,-24)&(25,24)

swap the numbers
think you accidently swapper the numbers for m and n
it shoult be (0, -7), (0, 7), (24, -25), (24, 25)

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

sadas123

1232 posts

sadas123

#46 h Apr 6, 2025, 2:08 AM • 1 Y

Y by PikaPika999

I got (4) possible values

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Apple_maths60

24 posts

Apple_maths60

#47 h Apr 6, 2025, 7:04 PM • 1 Y

Y by PikaPika999

AbhayAttarde01 wrote:

Apple_maths60 wrote:

I don't think (7,0)or (-7,0) would be a solution because if we put zero in the main equation we get √(-49)=m×m .
But √(-49) is not possible
So the answer must be 2
(25,-24)&(25,24)

swap the numbers
think you accidently swapper the numbers for m and n
it shoult be (0, -7), (0, 7), (24, -25), (24, 25)

Oh, ok got it. I actually did that mistake
Thank you!

This post has been edited 1 time. Last edited by Apple_maths60, Apr 6, 2025, 7:06 PM
Reason: .

Z K Y