Question

The sum of three numbers in A.P. is $15$ whereas sum of their squares is $83$. Find the product of the numbers.

Answer 1

Let the three numbers in A.P. be $a-d,a,a+d$
$Sum=3a=15\therefore a=5$
Sum of their squares $={(a-d)}^2+a^2+{(a+d)}^2=83$ or $3a^2+2d^2=83$
or $3a^2+2d^2=83$ or $d^2=83-3.25$
$\therefore d^2=4$ or $d=\pm 2.$
Hence the numbers are 3,5,7 or 7,5,3.