Question

1. If x= 2+√3, find the value of
X2+1/x2​

Answer 1

Given

x=2+3

To find,

x^2+1/x^2

solution

x=2+√3

1/x=1/2+√3×2-√3/2-√3

1/x=2-√3/2^2-√3^2

1/x=2-√3/4-3

1/x=2-√3

Now

x+1/x=2+√3+2-√3

x+1/x=2+2

x+1/x=4

And on squaring both sides

(x+1/x)^2=(4)^2

x^2+1/x^2+2=16

x^2+1/x^2=16-2

x^2+1/x^2=14

Hence

x^2+1/x^2=14

hope it's helpful

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