Question

Sum of two fractions is 10 and product is 5, what will be sum of inverses of fraction?

will get 20+ points

Answer 1

$\frac{p}{q} + \frac{m}{n} = 10 \: \: \: \: (1) \\ \frac{p}{q} \times \frac{m}{n} = 5 \: \: \: \: (2)$

From (1)

$\frac{pn + qm}{qn} = 10 \: \: \: \: (3)$

From (2)

$qn = \frac{pm}{5} \: \: \: \: (4)$

From (3) and (4)

$\frac{pn + qm}{ \frac{pm}{5} } = 10 \\ \frac{pn + qm}{ pm } = \frac{10}{5} \\ \frac{n}{m} + \frac{q}{p} = 2$

sum of inverses of fraction is 2