Question

If x = 3 - 2√2, find thevalue of √x+1+√x​

Answer 1

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

$\hookrightarrow \: \tt \: x = 3 - 2 \sqrt{2}$

$\star \: \: \: \: { \underline \blue{To \: \: Find }} :$

$\hookrightarrow \tt \: \sqrt{x} + \frac{1}{ \sqrt{x} } = {?}$

$\star \: \: \: \: { \underline \blue{Solution}} :$

$\dashrightarrow \: \tt\: x = 3 - 2 \sqrt{2}$

$\dashrightarrow \tt \: \sqrt x = \sqrt{3 - 2 \sqrt{2} }$

$\tt \red \: {Now,}$

$\looparrowright \: \: \tt\: \sqrt{x} + \frac{1}{ \sqrt{x} }$

$\tt \dashrightarrow \: \frac{x + 1}{ \sqrt{x} }$

$\tt \orange{ Putting \: \: value \: \: of \: \: x \: \: and \: \: √x}$

$\tt\dashrightarrow \: \frac{3 - 2\sqrt{2} + 1}{ \sqrt{(3 - 2\sqrt{2}) } }$

$\dashrightarrow \: \tt \frac{2(2 - \sqrt{2} )( 3 + 2 \sqrt{2}) }{ \sqrt{(3 - 2 \sqrt{2} )(3 + 2 \sqrt{2} )} }$

$\dashrightarrow \tt\: 12 + 8 \sqrt{2} - 3 \sqrt{2} - 2$

$\dashrightarrow \underline{ \boxed{ \mathfrak{ 10 - 5 \sqrt{2} }}}$

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$\star \: \: \blue{\mathbb{HOPE \: \: THIS \: \: IS \: \: HELPFUL}} \: \: \star$