Question

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Answer 1

hey mate here see this attachment paper

Answer 2

Solution:-

$\bold{STEP-BY-STEP-EXPLANATION:-}$

$L.H.S =\frac{3 - \sqrt{5} }{32 \sqrt{5} } \times \frac{3 - 2 \sqrt{5} }{3 - 2 \sqrt{5} } \\ \\ = \frac{(3 - \sqrt{5})(3 - 2 \sqrt{5}) }{(3) {}^{2} - (2 \sqrt{5}) {}^{2} }$

$= \frac{3(3 - 2 \sqrt{5}) - \sqrt{5}(3 - 2 \sqrt{5} ) }{9 - (4 \times 5)}$

$= \frac{9 - 6 \sqrt{5} - 3 \sqrt{5} + 10 }{ - 11} \\ \\ = \frac{19 - 9 \sqrt{5} }{ - 11} \\ \\ = \frac{ - (19 - 9 \sqrt{5}) }{11}$

$= \frac{ - 19 + 9 \sqrt{5} }{11} \\ \\ = \frac{ - 19 }{11} + \frac{9 \sqrt{5} }{11}$

$= \frac{9 \sqrt{5} }{11} - \frac{19}{11} <strong><u>=</u></strong><strong><u> </u></strong><strong><u>R.H.S</u></strong>\\ \\ \frac{9 \sqrt{5} }{11} - \frac{19}{11} = a \sqrt{5} \frac{ - 19}{11} \\ \\</h3><p></p><p>\huge\boxed{a = \frac{9}{11}}$

Hence, the value of 'a' = 9/11

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