Question

If x + 1/x= 4 find x^2+1/x^2 and x^3 + 1/x^3​

Answer 1

Answer:

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Explanation:

x + 1/x = 4 , squaring both sides we get x^2 + 1/x^2= 14, Similarly taking the power of 3 on both sides we get x^3 + 1/x^3 +3(x + 1/x) = 64 which implies x^3 + 1/x^3 = 52.

Now adding up the above two equations, we get

x^2 + 1/x^2 +x^3 + 1/x^3 = 66

it is given that x^2 + 1/x^3 =12 hence substituting this value in the above equation gives the answer of the question

i.e - x^3 + 1/x^2 + 12 = 66 which implies that x^3 + 1/x^2 = 54.

Hence the answer is 54