# Make x the subject of y(x^2+a^2)=a^3

• May 12th 2009, 10:51 AM
BabyMilo
Make x the subject of y(x^2+a^2)=a^3
Quote:

Make x the subject of y(x^2+a^2)=a^3
Many Thanks!
• May 12th 2009, 11:14 AM
HallsofIvy
Quote:

Originally Posted by BabyMilo
Many Thanks!

You want to solve $\displaystyle y(x^2+ a^2)= a^3$ for a.

Okay, multiplying the left side, $\displaystyle x^2y+ a^2y= a^3$ which is the same as $\displaystyle a^3- ya^2- x^2y= 0$. That is a cubic equation and there is a formula for the solution- unfortunately, it is very complicated.

Look at Cubic Formula -- from Wolfram MathWorld
• May 12th 2009, 11:21 AM
BabyMilo
I appreciate your help! But I am just making x the subject (like rearranging the equation). Many Thanks!
• May 12th 2009, 07:51 PM
mr fantastic
Quote:

Originally Posted by BabyMilo
I appreciate your help! But I am just making x the subject (like rearranging the equation). Many Thanks!

Divide by y. Subtract a^2. Take the square root.
• May 12th 2009, 10:56 PM
BabyMilo
Quote:

Originally Posted by mr fantastic
Divide by y. Subtract a^2. Take the square root.

so would it be? x=sq root of (a^3/y)-a^2 Many THanks!
• May 13th 2009, 01:34 AM
mr fantastic
Quote:

Originally Posted by BabyMilo
so would it be? x=sq root of (a^3/y)-a^2 Many THanks!

You need $\displaystyle \pm \sqrt{}$