Question

If n belong to I⁺ then find number of values of n for which n² - 36 is perfect square of an integer.

Answer 1

$$\begin{gathered} \mathrm{For}n=6 \\ {n}^2-36=6^2-36=0,\mathrm{which}\mathrm{is}\mathrm{a}\mathrm{perfect}\mathrm{square}. \\ Forn=10 \\ {n}^2-36={10}^2-36=64,\mathrm{which}\mathrm{is}\mathrm{a}\mathrm{perfect}\mathrm{square}. \\ \mathrm{Hence}\mathrm{there}\mathrm{are}\mathrm{two}\mathrm{possible}\mathrm{values}\mathrm{of}\mathrm{n}. \end{gathered}$$