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suppose x+1/x =3. evaluate x^3  + 1/x^3

I started by cubed both sides and now im lost. please help

 Dec 17, 2021
 #1
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x^3 + 1/x^3 = 21.

 Dec 17, 2021
 #2
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1)  Start with the equation  x + 1/x  =  3

      Multiply both sides by x, giving you a quadratic.

      Solve this quadratic (use the quadratic formula).

 

2)  Take each of the two answers from part 1) and place them into the expression:  x3 + 1/x3

 Dec 17, 2021
 #3
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(x + 1/x)3 = x3 + 3(x2)(1/x) + 3(x)(1/x2) + 1/x3 = x3 + 3x + 3/x + 1/x3

x3 + 1/x3 = (x + 1/x)3 - 3(x + 1/x) = 33 - 3(3) = 27 - 9 = 18.

 Dec 17, 2021

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