Question

if x²+1/x²= 7, find the value of x³+1/x³.

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Answer 1

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

7 = ( x+1/x)^2 - 2

x+1/x)^2 = 9

x+ 1/x = +-3

So x^3 + 1/x^3 = ( x+1/x)^3 - 3( x+1/x)

= 27 - 3(3) = 27-9 = 18

for x+1/x = -3

-27 -3( -3) = -27 +9 = -18

Answer 2

Step-by-step explanation:

(x+1/x)^2=x^2+1/x^2+2x1/x

(x+1/x)^2=7+2=9

x+1/x =3

similarly

(x+1/x)^3=x^3+1/x^3+3x1/x (x+1/x)

27=x^3+1/x^3+3 (3)

x^3+1/x^3=27-9=18

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