If x(square) plus y(square) is 8.and the froduvt is . what are x and y?

Given :-

To Find :-

Answer :-

Here we are given that,

x² + y² = 8 .

And ,

xy = 4

y = 4/x

So that ,

x² + (4/x)² = 8

x² +16/x² = 8

x⁴ + 16 = 8x²

x⁴ - 8x² + 16 = 0

Assume k² = x⁴ and k = x²

k² - 8k + 16 = 0

k² -4k -4k +16 = 0

k(k-4) -4(k-4) = 0

(k-4)² = 0

k = 4

So ,

k = x²

4 = x²

x = √4

x = ±2

Hence the required answer is ±2.