Question

If (x + 1/x) = 2, then find (x^2 + 1/x^2) and (x^4 + 1/x^4).

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Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Given,

x+1/x=2

Then,

x^2+1/x^2=(x+1/x)^2-2×x×1/x

=(2)^2-2

=4-2=2.

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

= (x^2+1/x^2)^2-2×x^2×1/x^2.

=(2)^2-2

=4-2=2.

Hence, x^2+1/x^2=2.

And, x^4+1/x^4=2.