Question

if x² - 3 = 5x, find x³ - 27/x³

Answer 1

Answer:

x^2 + 1/x^2 = 27

(x - 1/x)^2 = x^2 + 1/x^2 - 2×x×1/x

ie. (x - 1/x)^2 = 27 - 2 = 25

So. (x - 1/x) = 5

(x - 1/x)^3 = x^3 - 1/x^3 - 3×x×1/x(x - 1/x)

5^3 = x^3 - 1/x^3 - 3×5

125 = x^3 - 1/x^3 - 15

x^3 - 1/x^3 = 125 + 15

x^3 - 1/x^3 = 140 . So

3x^3 + 5x - 3/x^3 - 5/x

= 3(x^3 - 1/x^3) +5(x - 1/x)

= 3 × 140 + 5×5

=420 + 25 = 445

Ansh Jaiswal