Question

3 numbers are in ap and their sum is 18,sum of their squares is140.find the numbers​

Answer 1

let the three numbers Be
a+d,a,a-d
according to the first condition
a+d+a+a-d=18
3a=18
a=6
according to second condition
(a+d)^2+(a)^2+(a-d)^2=140
a^2+2ad+d^+a^2+a^2-2ad+d^2=140
3a^2+2d^2=140
3×(6)^2+2d^2=140
3×36+2d^2 =140
2d^2=140-108
d^2=32/2,
d^2=16
d=4

a-d=6-4=2
a=6
a+d=6+4=10
therefore the numbers are 2,6,10