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If x2+1/x2=34 then find the value of x3+1/x3-9

Posted by Aman Kumar 5 years, 8 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 8 months ago

We have, $x^{2}+\frac{1}{x^{2}}=34$
Also,
$\Rightarrow\left(x+\frac{1}{x}\right)^{2}=x^{2}+\frac{1}{x^{2}}+2 x^{2} \times \frac{1}{x^{2}}$
$\Rightarrow \left(x+\frac{1}{x}\right)^{2}=34+2$
$\Rightarrow \ n+\frac{1}{n}=\sqrt{36}=6$
Now,
$\Rightarrow \left(x+\frac{1}{x}\right)^{3}=x^{3}+\frac{1}{x^{3}}+3 x_{\times} \frac{1}{x}\left(x+\frac{1}{x}\right)$
$\Rightarrow 6^{3}=x^{3}+\frac{1}{x^{3}}+3 \times 6$
$\Rightarrow \quad x^{3}+\frac{1}{x^{3}}$ = 216 - 18
$x^{3}+\frac{1}{x^{3}}-9$ = 216 - 18 - 9
= 216 - 27
=189

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