The sum of two numbers is 45. The sum of their quotient and is reciprocal is 2.05, the product of the numbers is?  Pick one.
A) 300  B) 400  C) 500  D) 600  E) 700

Rationale: a + b = 45 a / b + b / a = 2.05 = > ( a ^ 2 + b ^ 2 ) / ab = 2.05 = > ( ( a + b ) ^ 2 − 2 ab ) / ab = 2.05 = > ( a + b ) ^ 2 = 2.05 ab + 2 ab = 4.05 ab = > ab = 45 ^ 2 / 4.05 = 500 answer : c
Answer: C