How do I use the quadratic formula to solve 2 + 5/(r-1) = 12/((r-1)^2)?

1 Answer
Aug 22, 2014

The answers are -3, 5/2.

You may be tempted to expand r-1, but let's use substitution: y=r-1

r=y+1

We have an NPV: r=1

2+5/y=12/(y^2)
2y^2+5y=12
2y^2+5y-12=0
y=(-5+-sqrt(5^2-4(2)(-12)))/(2(2))
=(-5+-sqrt(25+96))/4
=(-5+-sqrt(121))/4
=(-5+-11)/4
y=-4,3/2

You may be excited to get an answer and stop, but remember that we used substitution, so substitute back: r=y+1

r=-3,5/2

This does not conflict with the NPV, so the answer is good.

If you expand, you would have got:

2r^2+r-15=0

Then you would use the quadratic and the answer would be the same.