Question

2 to the power 2 x minus Y is equal to 128 and 2 to the power x + Y is equal to 32 then x squared plus y squared is equal to

Answer 1

$\textbf{Given:}$

$2^{2x-y}=128$

$2^{x+y}=32$

$\textbf{To find:}$

$x^2+y^2$

$\text{Consider}$

$2^{2x-y}=128$

$2^{2x-y}=2^7$

$\implies\bf\;2x-y=7$.......(1)

$2^{x+y}=32$

$2^{x+y}=2^5$

$\implies\bf\;x+y=5$.........(2)

$\text{Adding (1) and (2), we get}$

$3x=12$

$x=\dfrac{12}{3}$

$\implies\bf\;x=4$

$(2)\implies\;4+y=5$

$\implies\bf\;y=1$

$x^2+y^2=4^2+1^2=16+1=17$

$\therefore\textbf{The value of \bf\,x^2+y^2 is 17}$

Find more:

1.Solve each of the following systems of equations by the method of cross-multiplication:

ax + by = a²

bx + ay = b²

https://brainly.in/question/15918815

2.Solve each of the following systems of equations by the method of cross-multiplication:

(x/a) + (y/b) = a + b

(x/a²) + (y/b²) = 2

https://brainly.in/question/15918819

Answer 2

Step-by-step explanation:

2^2x-y=128

128 =2⁷

2x-y= 7

2^x+y=32

2⁵=32

x+y= 5

(2x-y) + (x+y)=12

3×=12

× =12/3

×= 4

y = 5-x

y=1

x²+y²=4²+1²

=16+1

= 17