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if x =2 -under root 5 ,find X2 + 1/x2

Posted by Navraj Singh Johal 8 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Payal Singh 8 years, 5 months ago

Given : x = {tex}2-\sqrt 5{/tex}

Now

{tex}{1\over x} = {1\over 2-\sqrt 5}{/tex}

Rationalize the denominator,

We get

{tex}{1\over x} = {1\over 2-\sqrt 5}\times {2+\sqrt 5\over 2+\sqrt 5}{/tex}

{tex}=> {1\over x} = {2+\sqrt 5\over (2)^2-(\sqrt 5)^2} {/tex}

{tex}=> {1\over x} = {2+\sqrt 5\over 4-5}= -2-\sqrt 5{/tex}

Now,

{tex}x^2+{1\over x^2}= (2-\sqrt 5)^2+(-2-\sqrt5)^2{/tex}

= {tex}4+5-4\sqrt5+4+5+4\sqrt5{/tex}= 18

1Thank You

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