Question

x+1/x=2+√3 find x^2+1/x^2​

Answer 1

Answer:

$Value \:of \:x^{2}+\frac{1}{x^{2}}=14$

Step-by-step explanation:

$x = 2+\sqrt{3}\:---(1)$

$\frac{1}{x}=\frac{1}{2+\sqrt{3}}\\=\frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}\\=\frac{2-\sqrt{3}}{2^{2}-(\sqrt{3})^{2}}\\=\frac{2-\sqrt{3}}{4-3}\\=2-\sqrt{3}\:--(2)$

$x+\frac{1}{x}\\=2+\sqrt{3}+2-\sqrt{3}=4\:--(3)$

$Now,\\x^{2}+\frac{1}{x^{2}}\\=(x+\frac{1}{x})^{2}-2\times x\times \frac{1}{x}\\=4^{2}-2\\=16-2\\=14$

Therefore,

$Value \:of \:x^{2}+\frac{1}{x^{2}}=14$

•••♪