Question

if x=2+√3 find the value of x2+1/x2​

Answer 1

Answer:

14 + 8 root 3

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Answer 2

Answer:

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

Step-by-step explanation:

$x = 2 + \sqrt{3} \\x + \frac{1}{x} = (2 + \sqrt{3} )+\frac{1}{(2 + \sqrt{3})}= \frac{(2 + \sqrt{3}) ^{2} +1}{(2 + \sqrt{3})}\\\\=>(x + \frac{1}{x})^2= (\frac{(2 + \sqrt{3}) ^{2} +1}{(2 + \sqrt{3})})^2\\=>x^2 +\frac{1}{x^2} +2 = (\frac{4+3 + 4\sqrt{3} +1 }{2+\sqrt{3} } )^2=(\frac{8+4\sqrt{3} }{2+\sqrt{3} } )^2=(\frac{4(2+\sqrt{3})}{2+\sqrt{3}} )^2=4^2=16\\=>x^2 +\frac{1}{x^2}= 16 - 2 = 14$