Question

the sum of three numbers in A.P. is 24 and the sum of their squares is 224. Find the number

Answer 1

Three no are
a+d a a-d
ATQ

Answer 2

let, the numbers be a-d,a,a+d
By given condition (a-d)+a+(a+b)=24
or 3a = 24
.°. a = 8
By second given condition
(a-d)²+a²+(a+d)²= 224
= (8-d)²+8²+(8+d)²=224
= 2(64+d²)= 224-64=160
=64+d=80=> d² = 16, d = ±4
.-. the required numbers are a-d,a,a+for 4,8,12