Question

If x^2+y^2=13 and xy=6 then find the value of x^4+y^4

Answer 1

Recall that (a + b)² = a² + 2ab + b².

Let a = x² and b = y². Then

(x² + y²)² = (x²)² + 2x²y² + (y²)²

⇒   x⁴ + y⁴ = (x² + y²)² - 2 (xy)²

Given that x² + y² = 13 and xy = 6, we have

x⁴ + y⁴ = 13² - 2×6² = 97