Question

Find three numbers in ap whsoe sum is 18 and product is 66

Answer 1

11.6.1=66and11+6+1=18

Answer 2

let the three numbers in A.P. be a-d ,a, a+d . So sum of these three numbers is 18=> a+d+a+a-d =18 => 3a=18 => a =6 . Product of these three numbers is 66 => (a-d)a(a+d) =66 =>
$({a}^{2} - {d}^{2})a = 66 = > \frac{66}{6} = 11 =$
${a}^{2} - {d}^{2} = {6}^{2} - {d }^{2} = > 11 = 36 - {d}^{2}$
$36 - 11 = 25 = {d}^{2} = > d = 5 \: or - 5$
So the numbers are 6+5,6,6-5 => 11,6,1 .