SOLUTION: I have a hard exponent quadratic question. 5x^2/3 + 2x^4/3 -13 =0 My first inclination was to rearrange the terms to... 2x^4/3 + 5x^2/3 -13 =0 This puts it in the right

Question 353894: I have a hard exponent quadratic question.
5x^2/3 + 2x^4/3 -13 =0
My first inclination was to rearrange the terms to...
2x^4/3 + 5x^2/3 -13 =0
This puts it in the right order for substitution / y= x^2/3
Thus... 2y^2 + 5y -13 =0
This is where I'm stuck. I don't know how to unfold the answer with the unusual powers.
Thanks for your help.
Neil
Found 3 solutions by Earlsdon, Alan3354, ewatrrr:
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Well, you are ok so far but now you can use the quadratic formula () to solve for y. In this problem, a = 2, b = 5, and c = -13, so...

When you evaluate this you will get:
or
Now you will need to substitute , so...
or
To find x, raise both sides of each solution to the (the reciprocal of ) power.
or Use your calculator to evaluate to get:
or
It would be advisable to check these solutions in your original equations.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
5x^2/3 + 2x^4/3 -13 =0
My first inclination was to rearrange the terms to...
2x^4/3 + 5x^2/3 -13 =0
This puts it in the right order for substitution / y= x^2/3
Thus... 2y^2 + 5y -13 =0
This is where I'm stuck. I don't know how to unfold the answer with the unusual powers.
Thanks for your help.
-------------------------
Solve your equation for y:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=129 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.58945417290014, -4.08945417290014. Here's your graph:

y = -5/4 � sqrt(129)/4
x^(2/3) = -5/4 � sqrt(129)/4
It's messy, but it's just arithmetic from here.
Cube both sides:
x^(2/3) = -5/4 + sqrt(129)/4
x^2 = (1/16)*(-515 + 51sqrt(129))

------------------
Can you do rest?

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
HI,
2x^4/3 + 5x^2/3 -13 =0
.
2x^4 + 5x^2 -39 =0
*Note: This is a bi-quadratic form of an equation. In General:
The bi-quadratic equation is ax4 + bx2 + c = 0 and as it can be writen as:.
.
has the roots:
.

.

.

.

.

.
or
or
or
RELATED QUESTIONS
hello I am having a hard time solving this equation, and would appreciate it if you would (answered by nerdybill)
I have a question on this problem 3(x-8)(2x^2+5x-4) after the 2x is suppose to be a... (answered by Alan3354)
Hey there, I have recently been set a simultaneous equations hwk that up till now I have... (answered by Alan3354)
Please help I need to know do these Quadriac Equations have a solution or not. And how to (answered by stanbon)
I'm having issues with these types of problems sinking in. -5x+3=x^2+2x, -5x+3-x^2+2x=0... (answered by josgarithmetic,addingup,ikleyn)
I need help with this question, I'll give the exact question. Question: Given that... (answered by stanbon)
Hi I was needing help on my math homework and i need a couple of problems solved. and I (answered by Alan3354)
I just took a math test and was disappointed to see that I got a "C." I had worked very... (answered by chessace)
Hi I have to solve the following rational inequality: 2/x+1 <= 4/x-3 The first thing I... (answered by ewatrrr,richwmiller)