The sum of two numbers is 45. The sum of their quotient and is reciprocal is 2.05, the product of the numbers is? Choices:
A) 300 B) 400 C) 500 D) 600 E) 700
a + b = 45   a/b+b/a = 2.05   =&gt;(a^2+b^2)/ab = 2.05   =&gt;((a+b)^2−2ab)/ab=2.05   =&gt;(a+b)^2 = 2.05ab + 2ab = 4.05ab   =&gt; ab = 45^2 / 4.05 = 500   ANSWER:500
<result>C</result>
The sum of two numbers is 45. The sum of their quotient and is reciprocal is 2.05, the product of the numbers is?