Question

Question :-
[tex]if \: \: x = \frac{1}{ \sqrt{7 + \sqrt{5} } } then \: find[/tex]
[tex]the \: value \: of \: {(x + \frac{1}{x} )}^{2} [/tex]

Please help me
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Answer 1

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf \dashrightarrow \: \bigg( \dfrac{1}{ \sqrt{7 + \sqrt{5} } } + \sqrt{7 + \sqrt{5} } \bigg) {}^{2} [/tex]

[tex]\qquad \sf \dashrightarrow \: \bigg( \dfrac{1}{ \sqrt{7 + \sqrt{5} } } \bigg ) {}^{2} + \bigg( \sqrt{7 + \sqrt{5} } \bigg) {}^{2} + 2 \cdot \dfrac{1}{ \sqrt{7 + \sqrt{5} } } \cdot \sqrt{7 + \sqrt{5} } [/tex]

[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{7 + \sqrt{5} } + 7 + \sqrt{5} + 2[/tex]

[tex]\qquad \sf \dashrightarrow \: \dfrac{49 + 7 \sqrt{5} + 7 \sqrt{5} + 5 + 14 + 2 \sqrt{5} }{7 + \sqrt{5} } [/tex]

[tex]\qquad \sf \dashrightarrow \: \dfrac{68+ 16 \sqrt{5} }{7 + \sqrt{5} } [/tex]