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If x2+1/x2=34 then find the value …

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

Posted by Aman Kumar 6 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 6 years, 3 months ago

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

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