SOLUTION: This is actually solving a problem that is quadratic in form. I am having lots of difficulties trying to figure this one out trying to substitute, but even sure if that is what I a

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: This is actually solving a problem that is quadratic in form. I am having lots of difficulties trying to figure this one out trying to substitute, but even sure if that is what I a      Log On


   

Question 258790: This is actually solving a problem that is quadratic in form. I am having lots of difficulties trying to figure this one out trying to substitute, but even sure if that is what I am supposed to do and totally stumped. Here is the problem:
(x-3)^2/5=(4x)^1/5
If I let u = (x-3)^1/3, it still doesn't quite make it into a quadratic as it then looks like:
u^2=(4x)^1/5
This is where I am stumped, not sure how to proceed after this since I can't use u to equal the 4x also as they are not like terms.
(and the exponents are fractions)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
%28x-3%29%5E%282%2F5%29+=+%284x%29%5E%281%2F5%29 Raise both sides to the 5th power.
%28%28x-3%29%5E%282%2F5%29%29%5E5+=+%28%284x%29%5E%281%2F5%29%29%5E5 Multiply the exponents on the inside of the parentheses by those on the outside.
%28x-3%29%5E2+=+%284x%29 Simplify.
x%5E2-6x%2B9+=+4x Subtract 4x from both sides.
x%5E2-10x%2B9+=+0 Factor this quadratic equation.
%28x-1%29%28x-9%29+=+0 Apply the zero product rule.
x-1+=+0 or x-9+=+0 so...
highlight%28x+=+1%29 or highlight%28x+=+9%29
Caution! Check the solutions by substituting into the given equation to discover any possible "extraneous" solutions..
%28x-3%29%5E%282%2F5%29+=+%284x%29%5E%281%2F5%29 Substitute x = 1.
%281-3%29%5E%282%2F5%29+=+%284%2A1%29%5E%281%2F5%29 Evaluate using a calculator.
%28-2%29%5E%282%2F5%29+=+%284%29%5E%281%2F5%29
1.3195079+=+1.3195079 OK for x=1.
%28x-3%29%5E%282%2F5%29+=+%284x%29%5E%281%2F5%29 Substitute x = 9.
%289-3%29%5E%282%2F5%29+=%284%2A9%29%5E%281%2F5%29 Evaluate.
6%5E%282%2F5%29+=+36%5E%281%2F5%29
2.0476725+=+2.0476725 OK for x = 9
Both solutions are valid!