Difference between the squares of two conterminous numbers

[kate]

The difference between the squares of two conterminous numbers is 36. Find the product of these two numbers.

[Guest]

suppose the numbers be a,a+1


according to question difference between their squares is 36

(a+1)^2-a^2=36
a^2+1^2+2(a)(1)-a^2=36
a^2+2+2a-a^2=36
2+2a=36
2a=36-2
2a=34
a=17
one number is 17
and other is 18 (17+1)
so the product of numbers is 17*18=306