If x = 3 + √5. Find the value of (x²+1/x²) ​

Answer:

If x= 2+sqrt3

then

1/x=2-sqrt3 (by rationaliztion)

then (x+1/x)^2 = X^2+(1/X)^2 +2*x*(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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