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

Answer:

17

Step-by-step explanation:

Given :

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

&

$2^{x + y} = 32$

To Find :

The value of $x^2 + y^2$

Solution :

We know that,

$128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 =2^7$

&

$32 = 2 \times 2 \times 2 \times 2 \times 2 =2^5$

Hence,

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

⇒ $2x - y = 7$ ...(i)

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

⇒ $x + y = 5$ ...(ii)

By adding (i) & (ii),

We get,

(i) + (ii) ⇒$(2x - y) + (x + y) = 7 + 5$

⇒ $3x = 12$ ⇒ $x = 4$,..

By substituting the value of x in equation (ii),

We get,

⇒ $4 + y = 5$

⇒ $y = 5- 4 = 1$

⇒ $y = 1$

_

∴ $x^2 + y^2 = (4)^2 + (1)^2 = 16 + 1 = 17$

Answer 2

Here ,

We are given with :

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

And we have to find:

The value of x²+y².

Steps :

For finding x²+y² we must have the value of x and y.

So firstly we will find out the value of x and y , then we will put those values in x²+y².

For Full Solution Refer To The Above Attachment !!

Here we will get x = 1 and y = 4.

And the value of x²+ y² = 17.