Question

How do you solve these:
A)90 = a + a^2
B)90 = a + 1/a
I thought the answers to both were infinite but apparently not! The book told me 9 and 81 for A and 0.011 and 89.0899 for B which both look right.

Answer 1

are they to be solved separately?

if so we can rewrite the first as\[a^2+a-90=0\]and can factor this to solve it

the next we can approach with\[a+\frac{1}{a}-90=0\to a^2-90a+1=0\]which we can apply the quadratic formula to.

Answer 2

Ok so by definition you changed the 2nd eq. to a polynomial correct? I'm curious as to when I should have this instinct.