Question

please dont spam it​

Answer 1

Solution:-Putting the value of x directly in the value which we have to find will make it more complicated,,and difficulty in solve....

As we can se

$3 - 2 \sqrt{2} = ( { \sqrt{2} - 1) }^{2} \: \\ so \: x \: will \:also \: be \: equal \: to \: ( { \sqrt{2} - 1)}^{2} \\ putting \: this \: value \: of \: x \: we \: get \\ \sqrt{x} + \frac{1}{ \sqrt{x} } = \sqrt{ { (\sqrt{2 } - 1) }^{2} } + \frac{1}{ \sqrt{ {( \sqrt{2} - 1) }^{2} } } \\ \sqrt{x} + \frac{1}{ \sqrt{x} } = \sqrt{2} - 1 + \frac{1}{ \sqrt{2} - 1 } = \frac{( { \sqrt{2} - 1) }^{2} + 1}{ \sqrt{2 } - 1} \\ = \frac{2 + 1 - 2 \sqrt{2} + 1 }{ \sqrt{2} - 1 } \\ = > \sqrt{x} + \frac{1}{ \sqrt{x} } = \frac{4 - 2 \sqrt{2} }{ \sqrt{2} - 1 } \\ takiing \: out \: 2 \sqrt{2} common \: from \: num \: \\ we \: get \\ \sqrt{x} + \frac{1}{ \sqrt{x} } = \frac{2 \sqrt{2}( \sqrt{2} - 1) }{( \sqrt{2} - 1) } = 2 \sqrt{2} \\ hence \: 2 \sqrt{2} is \: the \: right \: answer \\ (hope \: it \: helps)$