Question

If `2^(x + y) = 2x - y = sqrt(8)`, then x = ______ and y = ______.

Answer 1

If `2^(x + y) = 2x - y = sqrt(8)`, then x = `underlinebb(3/2)` and y = 0.

Explanation:

`2^(x + y) = sqrt(8) = 2^(3/2)`, so `x + y = 3/2`. 

Also `2x - y = sqrt(8) = 2sqrt(2)`. 

Solve the linear system

`x + y = 3/2`

`2x − y = 2sqrt(2)` 

Add: `3x = 3/2 + 2sqrt(2)`

⇒ `x = 1/2 + (2/3)sqrt(2)` 

Then `y = 3/2 - x = 1 - (2/3)sqrt(2)`.