Gracie has 5555 pet bunnies that love to eat whole carrots. She has 39393939 carrots to feed the bunnies. Gracie will use as man
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Suppose 
has two roots, reciprocals of one another. Call them 
, with 
.
Let's divide through
by 
for now. By the fundamental theorem of algebra, we can factorize as
Expand the RHS to get
so we must have
The first equation says and 
occur in a ratio of the negative sum of the roots of , while the third equation says that the first and last coefficients 
must be the same.
Let's divide through
Expand the RHS to get
so we must have
The first equation says