SOLUTION: Solve the equation by making an appropriate substitution 32) x^-2

SOLUTION: Solve the equation by making an appropriate substitution 32) x^-2 - 11x^-1 + 10 = 0 33)x^2/5 -x^1/5 -2=0

Question 1059480: Solve the equation by making an appropriate substitution
32) x^-2 - 11x^-1 + 10 = 0
33)x^2/5 -x^1/5 -2=0
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve the equation by making an appropriate substitution
32) x^-2 - 11x^-1 + 10 = 0
Let x^-1 = w
w^2 - 11w + 10 = 0
Factor::
(w-10)(w-1) = 0
w = 10 or w = 1
Solve for "x"::
x^-1 = 10 or x^-1 = 1
x = 1/10 or x = 1
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33)x^2/5 -x^1/5 -2=0
Let w = x^(1/5)
w^2 - w -2 = 0
(w-2)(w+1) = 0
w = 2 or w = -1
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x^(1/5) = 2 or x^(1/5) = -1
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x = 2^5 = 32 or x = (-1)^5 = -1
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Cheers,
Stan H.
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