Question

The difference between two number is $3$. Then difference between their squares is $54$. Find the numbers.

Answer 1

Let the two numbers be $a$ & $b$, such that $a>b$

So, $a-b=3$

$a^2-b^2=54$

$\to (a-b)(a+b)=54$

$\to 3(a+b)=54$

$\to (a+b)=18$

So, $2a=21$

$\to a=\frac{21}{2}$

$\to b=\frac{15}{2}$

So, the numbers are $\frac{21}{2},\frac{15}{2}$