If (x + 1/x ) = 7 and x > 1, what is the value of (x³ + 1/(x³) )?

If (x + 1/x ) = 7 and x > 1, what is the value of (x³ +…

If (x + $\frac{1}{x}$ ) = 7 and x > 1, what is the value of (x³ + $\frac{1}{x^3}$ )?

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 322.

(x + 1/x) = 7

Cubing both sides

(x + 1/x)³ = 7³

(a + b)³ = a³ + b³ + 3ab(a + b)

⇒ x³ + 1/x³ + 3 × x × 1/x(x + 1/x) = 343

⇒ x³ + 1/x³ + 3(7) = 343

⇒ x³ + 1/x³ = 343 - 21

⇒ x³ + 1/x³ = 322