Question

If x(x-2)=1 then the value of x^2+(1)/(x^2) is

Answer 1

Answer:

x(x - 2)= 1

x^2 - 2x - 1=0

Using splitting the middle term formula,

x^2 -(x+x) - 1 = 0

x(x - 1) + 1( x - 1) = 0

(x - 1)(x+1) = 0

x = 1 or -1

so, x^2+1/x^2= (-1)^2+1/(-1)^2

= 2/1

= 2

This is same for both the values of x.

Hope you are satisfied with the answer.

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