Question

Given that x-y =


`8√(2)`
and xy = 137,
where x and y are both positive,
find the value of x + y without finding x or y
​

Answer 1

x + y = 26

Explanation:

The idea is to express (x+y)^2 via given data, and then take square root of this expression (of this number).

It will be exactly (x+y).

So,

`(x+y)^(2) =(x-y)+4xy=(8*√(2) )^(2) + 4*137 = 64*2 + 4*137 = 676.`

`Therefore, (x+y) = √(676) =26`

Answer:
`x + y = 26.`