2021 AMC 10B Problems/Problem 2
Contents
Problem
What is the value of ?
Solution
Note that the square root of any square is always the absolute value of the squared number because the square root function will only return a positive number. By squaring both and
, we see that
, thus
is negative, so we must take the absolute value of
, which is just
. Knowing this, the first term in the expression equals
and the second term is
, and summing the two gives
.
~bjc, abhinavg0627 and JackBocresion
Solution 2
Let , then
. The
term is there due to difference of squares. Simplifying the expression gives us
, so
~ shrungpatel
Video Solution
https://youtu.be/HHVdPTLQsLc ~Math Python
Video Solution by OmegaLearn
Video Solution 3
~savannahsolver
Video Solution by TheBeautyofMath
https://youtu.be/gLahuINjRzU?t=154
~IceMatrix
Video Solution by Interstigation
https://youtu.be/DvpN56Ob6Zw?t=101
~Interstigation
See Also
2021 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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