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4x^3/4 = x^1/2Find x

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snowleopard | Student, Grade 9 | eNotes Newbie

Posted March 16, 2010 at 10:54 PM via web

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4x^3/4 = x^1/2

Find x

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neela | High School Teacher | Valedictorian

Posted March 16, 2010 at 11:42 PM (Answer #1)

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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.

Aliter:

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.

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isbeatbox | Student , Grade 11 | eNotes Newbie

Posted March 17, 2010 at 2:45 AM (Answer #3)

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4x^3/4=x^1/2

64x/4=2x/2

16x=x

16=2x

8=x  ...... I think

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