SOLUTION: a. Jull wants to make a substitution in the equation: x^(1/3)-36=9x^(1/6) in order to convert it to a quadratic equation. Give the substitution (in form t=...) and the resulting qu

Question 947349: a. Jull wants to make a substitution in the equation: x^(1/3)-36=9x^(1/6) in order to convert it to a quadratic equation. Give the substitution (in form t=...) and the resulting quadratic equation. Do not solve.
b. After making the substitution u=x^4 in the equation, Jaime found the solution u=16 and u=-4. Find the solution(s) for x.

Thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!

That shown above is not rendering to display well on my view.

Use this substitution:
and this gives you .

u=x^(1/6) and u^2=x^(1/3)

Jaime did not use the best choice for substitution.
Also remember, you are first solving for x^(1/6).
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

a. Jull wants to make a substitution in the equation: x^(1/3)-36=9x^(1/6) in order to convert it to a quadratic equation. Give the substitution (in form t=...) and the resulting quadratic equation. Do not solve.
b. After making the substitution u=x^4 in the equation, Jaime found the solution u=16 and u=-4. Find the solution(s) for x.
Thank you
a.

Let
Then , or
becomes: ------- Resulting quadratic equation after substitution of t for
b.
Since , and u = 16, and u = - 4
, with u = 16

Thus,
, with u = - 4

This is an EXTRANEOUS SOLUTION, since NO EXPRESSION raised to a power results in a negative (< 0) value
Therefore, only solution is:
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