Question

The sum of two numbers is 45. sum of their quotient and reciprocal is 2.05

Answer 1

Let the two numbers be 'a' and 'b'.

Since the sum of two numbers is 45.

So, a+b =45

Since, the sum of its quotient and its reciprocal is 2.05.

So, $\frac{a}{b}+\frac{b}{a}=2.05$

$\frac{a^{2}+b^{2}}{ab}=2.05$

Using the identity $(a+b)^{2}=a^{2}+b^{2}+2ab$

So, we get

$\frac{(a+b)^{2}-2ab}{ab}=2.05$

$\frac{(45)^{2}-2ab}{ab}=2.05$

$2025-2ab=2.05ab$

$2025=2ab+2.05ab$

$2025=4.05ab$

$ab = \frac{2025}{4.05}$

ab= 500

Therefore, the product of the two numbers is 500.