Question

Please tell Q no. 12 fast

Answer 1

$\frac{1}{ \sqrt{2} + \sqrt{3} - \sqrt{5} } + \frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} } = \frac{1}{ \sqrt{2} } \\ \\ using \: identity \: {x}^{2} - {y}^{2} = (x + y)(x - y) \\ \\ there \: will \: be \: square \: of \: \sqrt{2} \: and \: \sqrt{3} - \sqrt{5} \\ \\ \sqrt{2} square \: is \: 2 \: and \: square \: of \ \sqrt{3} - \sqrt{5} \: will \: give \: us \: \\ \\ 3 + 5 - 2 \times \sqrt{3} \times \sqrt{5} \\ 8 - 2 \sqrt{15} \\ \\ put \: values \: \\ \frac{1}{(2) - (8 - 2 \sqrt{15)} } = \frac{1}{ \sqrt{2} } \\ \\ \frac{1}{2 - 8 - 2 \sqrt{15} } = \frac{1}{ \sqrt{2} } \\ \\ \frac{1}{ - 6 - 2 \sqrt{15} } = \frac{1}{ \sqrt{2} } \\ \\ cross \: multiply \\ \sqrt{2} = - 6 - 2 \sqrt{15} \\ \\ 6 = - 2 \sqrt{15} - \sqrt{2}$