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4x^3/4 = x^1/2Find x
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High School Teacher
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We presume you want to solve 4x^(3/4) = x^(1/2). ( But kindly nor that 4x^3/4 = x^1/2 gives the meaning of (4x^3)/4 = (x^1)/2 , in which case x^3 = x/2 Or x= 0 or x = + sqrt (1/2) or x = -sqrt(1/2) shall be the solution for x.
To solve the above equation.
If we raise both sides to the 4th power , we get integral exponents. So,
[4x^(3/4)]^4 = [x^(1/2)] ^(4).
256x^3 = x^2. Or
256x^3-x^2 = 0. Or
x^2(256x -1) = 0 . Or
x^2 = 0, Or 256x-1 = 0.
x^2 = 0 gives x= 0
256x-1 = 0 gives x = 1/256.
Also 4x^(3/4) = x^(1/2). Divding both sides by x^(1/2).
4x^(1/4) = 1
x^(1/4) = 1/4 . S x = (1/4)^4.
Also you can go by x^(1/4) = t and solve for x = t^4.
Posted by neela on March 16, 2010 at 11:42 PM (Answer #1)
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