Question

Please help meeeeeeee​

Answer 1

$\\ \rm\Rrightarrow \left(x+\dfrac{1}{x}\right)^2$

$\\ \rm\Rrightarrow \left(\dfrac{x^2+1}{x}\right)^2\dots(1)$

• .Find x²

$\\ \rm\Rrightarrow \left(\dfrac{1}{\sqrt{2}+\sqrt{5}}\right)^2$

$\\ \rm\Rrightarrow \dfrac{1}{2+2\sqrt{10}+5}$

$\\ \rm\Rrightarrow \dfrac{1}{2\sqrt{10}+7}$

Now put in eq(1)

$\\ \rm\Rrightarrow \left(\dfrac{\dfrac{1}{2\sqrt{10}+7}+1}{\dfrac{1}{2\sqrt{10}+7}}\right)^2$

$\\ \rm\Rrightarrow \left(\dfrac{1+2\sqrt{10}+7}{2\sqrt{10}+7}\times (2\sqrt{10}+7)\right)^2$

$\\ \rm\Rrightarrow \left(\dfrac{2\sqrt{10}+8}{2\sqrt{10}+7}\times (2\sqrt{10}+7)\right)^2$

$\\ \rm\Rrightarrow \left(\dfrac{(2\sqrt{10}+8)\cancel{(2\sqrt{10}+7)}}{\cancel{2\sqrt{10}+7}}\right)^2$

$\\ \rm\Rrightarrow (2\sqrt{10}+8)^2$

$\\ \rm\Rrightarrow 40+32\sqrt{10}+64$

$\\ \rm\Rrightarrow 32\sqrt{10}+94$

More simplification (If required)

$\\ \rm\Rrightarrow 2^52^{\frac{1}{2}}\sqrt{5}+94$

$\\ \rm\Rrightarrow 2^{5+\frac{1}{2}}\sqrt{5}+94$

$\\ \rm\Rrightarrow 2^{\frac{11}{2}}\sqrt{5}+94$

$\\ \rm\Rrightarrow \sqrt{2^{11}}\sqrt{5}+94$

$\\ \rm\Rrightarrow \sqrt{2048(5)}+94$

$\\ \rm\Rrightarrow \sqrt{10240}+94$

Most accurate

$\\ \rm\Rrightarrow 101.19+94$

$\\ \rm\Rrightarrow 195.19$