SOLUTION: Solve the rational equation {{{x^3/16=x^6/2}}}

Question 190040: Solve the rational equation

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve the rational equation
x^3/16 = x^6/2
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Cross-multiply to get:
2x^3 = 16x^6
Rearrange:
16x^6 - 2x^3 = 0
Factor:
2x^3(8x^3-1) = 0
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x = 0 or 8x^3-1 = 0
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Solve 8x^3-1 = 0
Factor:
(2x-1)(4x^2+2x+1) = 0
x = 1/2 or 4x^2+2x+1 = 0
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Sole 4x^2+2x+1 = 0
x = [-2 +- sqrt(4 - 4*4*1)]/2
x = [-2 +- sqrt(-12)]/2
x = [-2 +- 2isqrt(3)]/2
x = [-1 +- isqrt(3)]
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Ans: x = -1+sqrt(3)i, x = -1-sqrt(3)i, x = 1/2 , x = 0 (multiplicity 3)
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