Question

Find three number in $A.P$. such that their sun is $24$ and the sum of their square is $200$

Answer 1

Let the numbers be $a-d,a,a+d$

$a-d+a+a+d=243a=24a=8{(a-d)}^2+{\left(a\right)}^2+{(a+d)}^2=2003a^2+2d^2=200192+2d^2=200d^2=4d=\pm 2$

So the numbers are

$8,10,12$ or $8,6,4$