If x=root2-root3. Find x+1/x

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Posted by Reena Karim 8 years, 7 months ago
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Payal Singh 8 years, 7 months ago
Given : {tex}x = \sqrt 2-\sqrt 3{/tex}
Then {tex}{1\over x} = {1\over \sqrt 2-\sqrt 3}{/tex}= {tex}{1\over \sqrt 2-\sqrt 3}\times {\sqrt 2+\sqrt 3\over \sqrt 2+\sqrt 3}{/tex}
= {tex}{\sqrt 2+\sqrt 3\over 2-3} ={\sqrt 2+\sqrt 3\over -1}{/tex}= {tex}-\sqrt 2-\sqrt 3{/tex}
To find : {tex}x+{1\over x}{/tex}= {tex}\sqrt 2-\sqrt 3-\sqrt 2-\sqrt 3=-2\sqrt 3{/tex}
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