Question

x²+y²+(1/x²)+(1/y²)=4 find x²+y²

Answer 1

(x^2 + 1/x^2 - 2) + (y^2 + 1/y^2 - 2) = 0 (subtracting 2 from both sides, twice)

(x - 1/x)^2 + (y - 1/y)^2 = 0

Therefore, (x - 1/x) = 0 and (y - 1/y) = 0 ( square of a number cannot be negative therefore they are each equal to 0.( i assumed x and y are real numbers not imaginary))

Hence, x^2 = y^2 = 1;

x^2 + y^2 = 2