First off, you're going to end up with 2 answers.
Alright so you have:
[tex] \frac{48}{b^2} = \frac{750}{b^5} [/tex]
You'll want to multiply both sides by b²
You'll end up with:
[tex]48 = \frac{750}{b^3} [/tex]
Multiply both sides by [tex]b^5[/tex]
Now you should have:
[tex]48b^5 = 750b^2[/tex]
Subtract 750b^2 from both sides.
Now:
[tex]48b^5 - 750b^2 = 0[/tex]
Factor the left side of the equation:
[tex]6b^2(2b-5)(4b^2+10b+25)=0[/tex]
Set both factors to 0:
[tex]2b - 5 = 0[/tex] [tex]4b^2+10b+25=0[/tex]
Your Answers:
b = 0 or b = [tex] \frac{5}{2} [/tex]
