Question

if x+1/x=4 find (x²+1/x²) and (x³+1/x³)​

Answer 1

Step-by-step 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.

Answer 2

Answer:

Step-by-step 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.