2017 AMC 10B Problems/Problem 4
Contents
Problem
Supposed that and are nonzero real numbers such that . What is the value of ?
Solution 1
Rearranging, we find , or . Substituting, we can convert the second equation into .
More step-by-step explanation:
.
We choose .
Solution 2
Substituting each and with , we see that the given equation holds true, as . Thus,
Solution 3
Let . The first equation converts into , which simplifies to . After a bit of algebra we found out , which means that . Substituting into the second equation it becomes - mathleticguyyy
Solution 4
Let . Then . So the desired result is . Select .
~hastapasta
Video Solution
https://youtu.be/ba6w1OhXqOQ?t=1059
~ pi_is_3.14
Video Solution
~savannahsolver
Video Solution by TheBeautyofMath
https://youtu.be/zTGuz6EoBWY?t=668
~IceMatrix
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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 |
2017 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 2 |
Followed by Problem 4 |
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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.