Question

if x=3+√8 then find the value of x^2+1/x^2

Answer 1

Hope it is useful for u !!

Thankyou☺

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

x = (3 + √8)

$\tt{\rightarrow\dfrac{1}{x}=\dfrac{1}{(3+\sqrt{8})}}$

$\tt{\rightarrow\dfrac{1}{(3+\sqrt{8})}\times\dfrac{(3-\sqrt{8})}{(3-\sqrt{8})}}$

$\tt{\rightarrow\dfrac{(3-\sqrt{8})}{3^2-(\sqrt{8}^{2})}}$

$\tt{\rightarrow\dfrac{(3-\sqrt{8})}{(9-8)}}$

= (3 - √8)

★Now :-

$\tt{\rightarrow x+\dfrac{1}{x}}$

= (3 + √8) + (3 - √8)

= 6

$\tt{\rightarrow (x+\dfrac{1}{x})^{2}}$

= 6²

= 36

$\tt{\rightarrow (x^{2}+\dfrac{1}{x})^{2}+2\times x\times\dfrac{1}{x}=36}$

$\tt{\rightarrow (x^{2}+\dfrac{1}{x})^{2}+2=36}$

$\tt{\rightarrow (x^{2}+\dfrac{1}{x})^{2}=36-2}$

= 34

★Here we get :-

${\boxed{\sf\:{(x^{2}+\dfrac{1}{x})^{2}=36}}}$