Question

If $2^{2x-y}=32$ and $2^{x+y}=16$ then $x^2+y^2$ is equal to

• A. 9
• B. 10
• C. 11
• D. 13

Answer 1

Answer: (B)

10

Given,

$2^{2x-y}=32$

$2^{x+y}=16$

these equations can be writtn as

$2^{(2x-y)}=2^5$

$\Rightarrow 2x-y=5$.......................eq1

$2^{x+y}=2^4$

$\Rightarrow x+y=4$...........................eq2

on adding both equations

$x+y=4$

$2x-y=5$

_______________________

$3x=9$

$x=3$

putting the value of x we get the value of y

$3+y=4$

$y=1$

putting the values of x and y we get

$x^2+y^2$

$3^2+1^2=9+1=10$