Question

If x^2+1/x^2=51;find the value of x^3-1/x^3

Explain it clearly​

Answer 1

Answer:

a³ b³ = (a - b)(a² + b² + ab)

So,

+ - + - (- - -) ( ~² + + 1 x³ x³ X + + + × ²) 1 x²

- (₁ - 1) (~² + 3 + ¹) 1 x² - (x-²)(1+1) = X X

- 52 (x-1)

Now,

(x - ²)² =

= 512 49

1 X X 49 = 7

Therefore,

1 x³ (x-²) = 52

= 52 x 7

= 364