Question

The sum of three numbers in AP is $21$ and their product is $231.$ Find its numbers.

Answer 1

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

$\Rightarrow a-d+a+a+d=21$

$\Rightarrow 3a=21$ $\Rightarrow a=7$

(a-d)(a)(a+d)=231

$\Rightarrow (a^2-d^2)\left(a\right)=231$

$\Rightarrow 49-d^2=\frac{231}{7}=33$

so $d^2=16,d=\pm 4$

No. 3,7,11 or 11,7,3