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Solve the value of (x3-1/x3),if x2+1/x2=82/9

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Solve the value of (x3-1/x3),if x2+1/x2=82/9

Posted by Smaty Nickke Singh 7 years, 2 months ago

UP Board > Class 09 > गणित

2 answers

Rashika Soni 7 years, 2 months ago

5282582

Payal Singh 7 years, 2 months ago

Given : {tex}x^2+{1\over x^2}={82\over 9}{/tex}

To find : {tex}x^3-{1\over x^3}{/tex}

Solution:

We know,

{tex}(x-{1\over x})^2= x^2+{1\over x^2}-2{/tex}

{tex}=> (x-{1\over x})^2={82\over 9}-2{/tex}

{tex}=> (x-{1\over x})^2={64\over 9}{/tex}

{tex}=> (x-{1\over x})={8\over 3}{/tex}

Also,

{tex}=> (x^3-{1\over x^3})= (x-{1\over x})(x^2+{1\over x^2}+1){/tex}

{tex}=> (x^3-{1\over x^3})= ({8\over 3})({82\over 9}+1){/tex}

{tex}=> (x^3-{1\over x^3})= ({8\over 3})({91\over 9}) {/tex}

{tex}=> (x^3-{1\over x^3})= {728\over 27}{/tex}

ANSWER

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