If 2x + 2/x = 5, then the value of ( x³ + 1/(x³) + 2) will be:

If 2x + 2/x = 5, then the value of ( x³ + 1/(x³) + 2) will…

If 2x + $\frac{2}{x}$ = 5, then the value of ( x³ + $\frac{1}{x^3}$ + 2) will be:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. $\frac{81}{8}$ .

Given that

If 2x + $\frac{2}{x}$ = 5,

⇒ x + $\frac{1}{x}$ = 5/2

Cube on both sides

⇒ x³ + $\frac{1}{x^3}$ + 3 (x + $\frac{1}{x}$ ) = 125/8

⇒ x³ + $\frac{1}{x^3}$ + 3 × (5/2) = 125/8

⇒ x³ + $\frac{1}{x^3}$ = 125/8 - 15/2

⇒ x³ + $\frac{1}{x^3}$ = (125 - 60)/8 = 65/8

Hence, x³ + $\frac{1}{x^3}$ + 2 = 65/8 + 2 = $\frac{81}{8}$