Question

$if \\ p (x) = x^{2} - \sqrt[2]{2x+1} \\ then\\ find\\ the \\ value \\ of \\ p\sqrt[2]{2}$

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{\implies{p(\sqrt2)=2-\sqrt{2\sqrt2+1}}}$

$\sf\orange{Given:}$

$\sf{px=x^{2}-\sqrt{2}{2x+1}}$

$\sf\pink{To \ find:}$

$\sf{p(\sqrt[2]{2})}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{\sqrt[2]{2} \ also \ can \ be \ written \ as \ \sqrt2}$

$\sf{\implies{p(x)=x^{2}-\sqrt{2x+1}}}$

$\sf{\implies{p(\sqrt2)=\sqrt2^{2}-sqrt{2\times2+1}}}$

$\sf\purple{\implies{p(\sqrt2)=2-\sqrt{2\sqrt2+1}}}$

Answer 2

$\purple{\underline{\underline{\pink{Que}\red{stion:}}}}$

$\rm{If \ p (x) = x^{2} - \sqrt[2]{2x+1} \ then \ find \ the }$

$\rm{value \ of \ p\sqrt[2]{2}}$

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$\pink{\underline{\underline{\orange{Ans}\green{wer:}}}}$

$\sf\red{\implies{p(\sqrt2)=2-\sqrt{2\sqrt2+1}}}$

_________________________________________

$\sf\underline\blue{Given:}$

$\rm{p (x) = x^{2} - \sqrt[2]{2x+1}}$

_________________________________________

$\sf\purple{To \ find:}$

$\sf{p(\sqrt[2]{2})}$

________________________________________

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{\sqrt[2]{2} \ also \ can \ be \ written \ as \ \sqrt2}$

$\sf{\implies{p(x)=x^{2}-\sqrt{2x+1}}}$

$\sf{\implies{p(\sqrt2)={(\sqrt{2})}^2-\sqrt{2\sqrt2+1}}}$

$\sf\green{\implies{p(\sqrt2)=2-\sqrt{2\sqrt2+1}}}$

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$\rm\pink{Hope \ it \ helps \ :))}$