Question

x+1/x=8 find x^2+1/x^2,x^3+1/x^3​

Answer 1

x+1/x = 8 -----------(1)

squaring both side we get

x^2 +1/x^2 +2×x×1/x = 64

x^2 + 1/x^2 +2 =64

x^2+1/x^2 = 64-2 = 62 Answer (i)

Now ,

x+1/x = 8

Cubing both sides , we get

x^3 +1/x^3+ 3x ×1/x ( x+1/x) = 8^3

x^3 +1/x^3 +3(x+1/x) = 512 ---------(2)

Substituting (1) in (2) ,

x^3 + 1/x^3 + 3×8 = 512

x^3 +1/x^3 = 512-24 = 488 Answer (ii)

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