Question

Find three numbers in A.P. such that their sum is $24$ & the sum of their square is $200$.

Answer 1

let the $3$ numbers be

$a-d,a,a+d$

Sum $=24$

if $3a=24$

$a=8$

$\therefore$ the numbers are

$(8-d),8,(8+d)$

Sum of squares $a=200$

$\Rightarrow (8-d{)}^2+8^2+(8+d^2)=200$

$\Rightarrow 3\left(8^2\right)+2d^2=200$

$\Rightarrow 2d^2=8\Rightarrow d^2=4\Rightarrow d=2$

$\therefore$ The $3$ numbers are $(8-2),8,(8+2)$

$\Rightarrow 6,8,10$