Question

If x+ 1/x = -2 then find x3 + 1/x^3​

Answer 1

Answer:

6/x

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Answer 2

Answer:

• Given

$x + \frac{1}{x} = - 2$

• To find
• $x {}^{3} + \frac{1}{x {}^{3} }$

$(x + \frac{1}{x} ) {}^{3} = ( - 2) {}^{3} \\ x {}^{3} + (\frac{1}{x} ) {}^{3} + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = - 8 \\ \\ x {}^{3} + \frac{1}{x {}^{3} } + 3( - 2) = - 8 \\ x {}^{3} + \frac{1}{x {}^{3} } - 6 = - 8 \\ x {}^{3} + \frac{1}{x {}^{3} } = - 8 + 6 \\ x {}^{3} + \frac{1}{x {}^{3} } = - 2$