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Identity (x+y)(x-y)

If x=2+√3 the...

Question

If x=2+√3 then find x²+1÷x²

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Solution

If x= 2+sqrt3
then
1/x=2-sqrt3 (by rationaliztion)
then (x+1/x)^2 = X^2+(1/X)^2 +2x(1/X)
that is (2+sqrt3 +2-sqrt3)^2=x^2 +(1/x)^2+2
4^2 -2=x^2+(1/x)^2
i.e, 14 is the answer

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