Question

If root x+1/root x= 7,
Find (x^2+1/x^2)

Answer 1

Solution :

Given,

√x + 1/√x = 7

Squaring both sides, we get

(√x + 1/√x)² = 7²

or, (√x)² + (2 * √x * 1/√x) + (1/√x)² = 49

or, x + 2 + 1/x = 49

or, x + 1/x = 49 - 2

or, x + 1/x = 47

Again, squaring both sides, we get

(x + 1/x)² = 47²

or, x² + (2 * x * 1/x) + (1/x)² = 2209

or, x² + 2 + 1/x² = 2209

or, x² + 1/x² = 2209 - 2

or, x² + 1/x² = 2207

Therefore, x² + 1/x² = 2207