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Math Help - Solving Equations Quadratic In Form (By Substitution?)

  1. #1
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    Solving Equations Quadratic In Form (By Substitution?)

    I know how to solve by substituting in some instances. The only times I've done it is with examples like this (x +1)^2/3 = (x + 1)^1/3

    With this problem since (x+1)^2/3 is [(x+1)^1/3]^2 you can just substitute "u" for the whole thing leaving you with u^2 = u. You would then bring everything to one side and solve the equation from there.

    The problem I'm having trouble with though looks a bit different.

    (x-3)^2/5 = (4x)^1/5

    Now the exponent 2/5 is the square of the exponent 1/5 but x-3 & 4x don't match so you shouldn't be able to just replace them with u.

    Anyone know where I should start?
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  2. #2
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    Re: Solving Equations Quadratic In Form (By Substitution?)

    Hello, street1030!

    A sneaky one! . . . It doesn't involve substitution.


    (x-3)^{\frac{2}{5}} \:=\: (4x)^{\frac{1}{5}}

    Raise both sides to the 5th power: . (x-3)^2 \:=\:4x

    And we have: . x^2 - 6x + 9 \:=\:4x \quad\Rightarrow\quad x^2 - 10x + 9 \:=\:0

    Got it?
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  3. #3
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    Re: Solving Equations Quadratic In Form (By Substitution?)

    AH! Didn't think of that. Thanks a bunch. Think this will help me with a few more also.
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