SOLUTION: I need to solve for a in the equation V = xyz, where {{{x = 2/(1+a)}}}, {{{y = 2/(1+a)}}}, and {{{z = -1/a}}}. This comes from a real world research problem I am working on, min

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I need to solve for a in the equation V = xyz, where {{{x = 2/(1+a)}}}, {{{y = 2/(1+a)}}}, and {{{z = -1/a}}}. This comes from a real world research problem I am working on, min      Log On


   

Question 31315: I need to solve for a in the equation V = xyz,
where x+=+2%2F%281%2Ba%29, y+=+2%2F%281%2Ba%29, and z+=+-1%2Fa.
This comes from a real world research problem I am working on, minimizing the area of a rectangle while keeping the volume constant.
Here is the final problem.
we need to get (a) on left side in units of (V) to right side from this:
V+=+%28-1%2Fa%29%282%2F%281%2Ba%29%29%282%2F%281%2Ba%29%29
Thank you for your help!
Found 2 solutions by stanbon, troyapplehelen:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a(1+a)^2=-4/V
You can't isolate "a" alone.
Cheers
Stan H.

Answer by troyapplehelen(46) About Me  (Show Source):
You can put this solution on YOUR website!
1. xyz=(-1/a)(4/(1+a)^2)
V=(-4)/(a(1+a)^2)
2. -v/4 = 1/(a(1+a)^2) because multiply with negative (-1/4) on both sides.
3. then, (a(1+a)^2) is (-4/v) it's the reciprocal.