Question

Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9.

Answer 1

Given:

(1/x) - (1/y) = (1/3)  

(1/x²) + (1/y²) = (5/9)

(A + B) ² = A² + 2AB + B²  

A2+B2 = 5/9

2AB=4/9

(A + B) ² = (5/9) + (4/9) = 1

When A+B=1

A-B=1/3  

Then the value of x, y = 3/2, 3

When A+B=-1

A-B=1/3 then the value of x, y = -3,-3/2