This question was previously asked in

GATE PI 2021 Official Paper

Option 2 : 7

__Concept:__

**Integers: **Integers are the positive numbers that can be negative, positive, and zero but cannot be fractions

**Examples: .......-2,-1,0,1,2.......**

__Calculation:__

__Given:__

** \(\frac{p}{q}\ +\ \frac{q}{p}\ =\ 3\)**.........

Where** p **and** q** are **positive integers**

Now by squaring on both sides of equation (1) we get

\(\left ( \frac{p}{q}\ +\ \frac{q}{p} \right )^2\ =\ 3^2\)

\(\frac{p^2}{q^2}\ +\ \frac{q^2}{p^2}\ +\ 2\ \times\ \frac{p}{q}\ \times\ \frac{q}{p}\ =\ 9\)

\(\frac{p^2}{q^2}\ +\ \frac{q^2}{p^2}\ +\ 2\ \ =\ 9\)

∴ \(\frac{p^2}{q^2}\ +\ \frac{q^2}{p^2}\ =\ 7\)