Question

Please answer quickly

Answer 1

QUESTION :–

• If x² - 8x + 1 = 0 then find x² + 1/x² .

ANSWER :–

62

EXPLANATION :–

Given :–

A quadratic equation x² - 8x + 1 = 0.

To find :–

x² + 1/x²

Solution :–

• We know a property –

☛ (a+b)² = a² + b² + 2ab

• So that –

=> (x+1/x)² = x² + 1/x² + 2(x)(1/x)

=> (x+1/x)² = x² + 1/x² + 2

=> (x² + 1/x²) = (x+1/x)² - 2

=> x² + 1/x² = [(x²+1)/x]² - 2 ---------(1)

• According to the question –

=> x² - 8x + 1 = 0

We should write this as –

=> x² + 1 = -8x

• Now put the value of (x² + 1) in equation (1) –

=> x² + 1/x² = [ (-8x)/x ]² - 2

=> x² + 1/x² = 64 - 2 = 62

Hence , x² + 1/x² = 62