Question 1086799
x^2 + 1/x^2 = 102
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x^4 + 1 = 102x^2, for x not = 0
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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
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x = + or - 10.099
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x^3 - 1/x^3 = ? 
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1) (10.099)^3 - 1/(10.099)^3 = 1029.994
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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
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(10.099)^2 + 1/(10.099)^2 = 102
101.999 = 102
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(-10.099)^2 + 1/(-10.099)^2 = 102
101.999 = 102
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our answer checks
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