BDMO National Junior 2018/4

[nahin munkar]

The squares of three positive numbers add up to $2018$. The biggest of these three numbers is the sum of the smaller two. If the difference between the smaller two numbers is $2$, what is the difference between the cubes of the smaller two numbers?

[samiul_samin]

Suppose the biggest number is $c$
The second highest is $a$
And smallest is $b$
Now
$a^2+b^2+c^2=2018$
$a^2+b^2+(a+b)^2=2018$
$a^2+b^2+ab=1009$
$(a-b)(a^2+ab+b^2)=2×1009$
$a^3-b^3=2018$


Given that,
$a+b=c$
$a-b=2$