Question

please answer me if you know

Answer 1

hey !! here's ur answer :-)

[I would have solved on paper but right now I don't have a paper and a pen ]

now come to the question :-

$x = \frac{ \sqrt{5 } - 2}{ \sqrt{5} + 2}$
so at first we will rationalize the denominator of the equation.
$x = \frac{ \sqrt{5} - 2}{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2} \\ \\ x = \frac{( \sqrt{5} - 2) {}^{2} }{( \sqrt{5} ) {}^{2} - (2) {}^{2} } \\ \\ x = \frac{5 - 4 \sqrt{5 } + 4}{5 - 4} \\ \\ x = \frac{9 - 4 \sqrt{5} }{1} = 9 - 4 \sqrt{5}$

now ,we have to find the value of

(i) x+1/x

$\frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} } \times \frac{9 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ \frac{9 + 4 \sqrt{5} }{81 - 80} = 9 + 4 \sqrt{5}$

so,
$x + \frac{1}{x} = 9 - 4 \sqrt{5} + 9 + 4 \sqrt{5} \\ x + \frac{1}{x} = 18$

(ii)
$(x + \frac{1}{x} ) {}^{2} = x {}^{2} + \frac{1}{x} {}^{2} + 2 \times x \times \frac{1}{x} \\ \\ (18) {}^{2} = x {}^{2} + \frac{1}{x} {}^{2} + 2 \\ \\ x {}^{2} + \frac{1}{x} {}^{2} = 324 - 2 \\ \\ x {}^{2} + \frac{1}{x} {}^{2} = 322$

hope it helps :-)

#thankyou