Question

if 2(x^2-1)=5x then x^3+1/x^3​

Answer 1

Answer:

63/8

x³ - 1/x³ = 63/8

Step-by-step explanation:

Given,

2(x² + 1) = 5x

→ 2x² + 2 = 5x

→ 2x² - 5x + 2 = 0

→ 2x² - 4x - x + 2 = 0

→ 2x(x -2) - 1(x-2) = 0

→ (x-2)(2x-1) = 0

→ x = 2, 1/2

Now, Put the values of "x' in x³ - 1/x³.

For x = 1/2

→ (1/2)³ - 1/(1/2)³

→ 1/8 - 8 = (1 - 64)/8 = -63/8

For x = 2

→ (2)³ - 1/(2)³

→ 8 - 1/8

= 63/8

So, for x = 1/2

x³ - 1/x³ = -63/8

and, for x = 2

x³ - 1/x³ = 63/8