Question

If x =√3 +√2/√3-√2 then find x4 +1/x4

Answer 1

Answer:

9602

Explanation:

$x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\\\\x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}\\\\x=\frac{(\sqrt{3}+\sqrt{2})^2}{(\sqrt{3})^2-(\sqrt{2})^2}\\\\x=5+2\sqrt{6}\\\\Similarly\\\\\frac{1}{x}=5-2\sqrt{6}$

$Now\\\\x^2=49+20\sqrt{6}\\\\And\\\\\frac{1}{x^2}=49-20\sqrt{6}\\\\Now\\(x^2+\frac{1}{x^2})^2=x^4+\frac{1}{x^4}+2\\\\x^4+\frac{1}{x^4}=98^2-2= 9602$

Hope it Helps