solve the equation by introducing a substitution that transforms the equation to quadratic form........ x^2/3 + 4x^1/3 = 0

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- Jan 28th 2009, 06:12 PMJshizza1228algebra equation
solve the equation by introducing a substitution that transforms the equation to quadratic form........ x^2/3 + 4x^1/3 = 0

- Jan 28th 2009, 06:24 PMmr fantastic
- Jan 28th 2009, 06:25 PMSoroban
Hello, Jshizza1228!

Quote:

Solve the equation by introducing a substitution that transforms

the equation to quadratic form: .$\displaystyle x^{\frac{2}{3}}+ 4x^{\frac{1}{3}} \:= \:0$

We have: .$\displaystyle \left(x^{\frac{1}{3}}\right)^2 + 4\left(x^{\frac{1}{3}}\right) \:=\:0$

Let $\displaystyle z \:=\:x^{\frac{1}{3}}$

. . and we have: .$\displaystyle z^2 + 4z \:=\:0$

Got it?