SOLUTION: If x^2 + 1/x^2 =102, find the value of x^3

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Question 1086799: If x^2 + 1/x^2 =102, find the value of x^3 - 1/x^3
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website!
x^2 + 1/x^2 = 102
:
x^4 + 1 = 102x^2, for x not = 0
:
x^4 -102X^2 +1 = 0
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let u = x^2, then
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u^2 -102u = -1
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complete the square
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u^2 -102u + 2601 = 2601 -1
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(u -51)^2 = 2600
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take square root of both sides of =
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u - 51 = 50.99
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u = 51 + 50.99 = 101.99
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u = x^2, then
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x^2 = 101.99
:
x = + or - 10.099
:
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x^3 - 1/x^3 = ?
:
1) (10.099)^3 - 1/(10.099)^3 = 1029.994
:
2) (-10.099)^3 - 1/(-10.099)^3 = −1029.994
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check answers for x
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x^2 + 1/x^2 = 102
:
(10.099)^2 + 1/(10.099)^2 = 102
101.999 = 102
:
(-10.099)^2 + 1/(-10.099)^2 = 102
101.999 = 102
:
our answer checks
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Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.

If = 102, then - 2 + = 102 - 2 = 100, or = 100, which implies = 10 or = -10. If = 10 then = 1000 = = - = - = - 3*10. It implies = 1030. If = -10 then = -1000 = = - = - = - 3*(-10) = + 30. It implies = -1000 - 30 = -1030.

Answer. Under the given condition, the expression    may have two values: 1030 or -1030.

Solved.

Two lessons to learn from this solution

    1. You do not need to solve equations to get the answer.

    2. The approach the tutor @rothauserc took to solve the problem is WRONG.

SOLUTION: If x^2 + 1/x^2 =102, find the value of x^3 - 1/x^3