If for a non-zero x, 7x²+ 5x + 7 = 0, then the x³ + 1/(x³) is ___.

If for a non-zero x, 7x²+ 5x + 7 = 0, then the x³ + 1/(x³)…

If for a non-zero x, 7x²+ 5x + 7 = 0, then the x³ + $\frac{1}{x^3}$ is _______________.

Show answer & explanation

Correct answer: D

Explanation

The correct answer is Option 4 i.e. $\frac{610}{343}$ .

7x²+ 5x + 7 = 0....(1)

Divide the equation by x

7x + 5 + $7\over x$ = 0

⇒ 7x + $7\over x$ = -5......(2)

⇒ x + $1\over x$ = $-5\over7$

x³ + $1\over x^3$ = (x + $1\over x$ )³ - 3(x + $1\over x$ )

⇒ x³ + $1\over x^3$ = ( $-5\over7$ )³ - 3( $-5\over7$ )

⇒ $-125\over343$ + $15\over7$ = $-125+735\over343$ = $\frac{610}{343}$