NIELIT 2019 Feb Scientist D - Section D: 5

Question

How many pair of natural numbers are there, the differences of whose squares is $45$ ? 

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Let first number be $x$, and the second number be $y.$

$(x^{2} - y^{2}) = 45$
$\implies (x - y)(x + y) = 45$

The factors of $45$ are $15, 3, 9, 5, 1$ and $45$

Hence, the possible pairs of numbers are $(9,6), (7,2)$ and $(23,22).$

$\therefore$ The number of such pairs $= 3.$

The correct answer is $(C).$

Answer 2

$3$ pair are there :$(9,6),(7,2),(22,23)$