2 rational numbers are added. The sum is 1/4 more than the product. What are the rational numbers?
2 Answers
If one is
Explanation:
Given:
#alpha+beta-alphabeta-1/4 = 0#
Then:
#beta(alpha-1)=alpha-1/4#
So:
#beta = (alpha-1/4)/(alpha-1) = (alpha-1+3/4)/(alpha-1) = 1+3/(4(alpha-1))#
There are any number of pairs than can be calculated from the given relationship. Two are derived below.
Explanation:
Let A and B be the numbers. Then from the relationships we have this equation.
CHECK:
Let's try it with A = 2
CHECK: