Question

can anyone answer this question plz.
I know the answer , but I don't know how to solve it , so plz send the explanation .

Answer is (2) , plz send the explanation​

Answer 1

Step-by-step explanation:

x = 1/(3-√5) (given)

$= \frac{1}{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ \\ \\ = \frac{3 + \sqrt{5} }{4}$

$\implies x = (3+√5)/4$

and 1/x = 3-√5

Now,

$(\sqrt{x} + \frac{1}{ \sqrt{x} }) {}^{2} = x + \frac{1}{x} + 2 \\ \\ = \frac{3 + \sqrt{5} }{4} + (3 - \sqrt{5} ) + 2 \\ \\ = \frac{3 + \sqrt{5} + 4(3 - \sqrt{5}) + 8 }{4} \\ \\ = \frac{3 + \sqrt{5} + 12 - 4 \sqrt{5} + 8 }{4} \\ \\ = \frac{23 - 3 \sqrt{5} }{4} \\ \\ = \frac{46 - 6 \sqrt{5} }{8} \\ \\ = \frac{45 + 1 - 6 \sqrt{5} }{8}$

$\implies \frac{(3 \sqrt{5 - 1}) {}^{2} }{(2 \sqrt{2}) {}^{2} } = ( \frac{3 \sqrt{5 - 1} }{2 - \sqrt{2} } ) {}^{2} \\ \\ \implies( \sqrt{x + \frac{1}{ \sqrt{x} } } ) {}^{2} = ( \frac{3 \sqrt{5} - 1 }{2 \sqrt{2} } ) {}^{2} \\ \\ \implies \sqrt{x} + \frac{1}{√x} = \frac{3 \sqrt{5} - 1 }{2 \sqrt{2} }$

Therefore, option (2) is correct.

Answer 2

Answer:

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