Question

Find x3+1/x3 if x+1/x = -6​

Answer 1

Answer:

the answer of this question is present in the following picture

Answer 2

AnswEr :

⋆ ɢɪᴠᴇɴ : $\sf\ x + \frac{1}{x} = -6$

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$\scriptsize\qquad\dag\sf\ cubing \: both \: sides$

$\sf\ : \implies\big( x + \frac{1}{x} \big)^3 = (-6)^3\\\\\scriptsize\qquad\dag\sf\ using (a+b)^3 = a^3 + b^3 + 3(a + b)\\\\\sf\ : \implies\big( x^3 + \frac{1}{x^3} + 3( x + \frac{1}{x}) \big)= -216\\\\\\\\\sf\ : \implies\big( x^3 + \frac{1}{x^3} + 3(-6) \big) = -216\\\\\\\sf\ : \implies\big( x^3 + \frac{1}{x^3} \big) = -216 + 18\\\\\\\sf\ : \implies\big( x^3 + \frac{1}{x^3} \big) = -198\\\\\\\ : \implies\boxed{\bf\big( x^3 + \frac{1}{x^3} \big) = -198}$