if the sum of four numbers in A.P is24 and sum of thier squares is 164.then those numbers are

they are 3,5,7,9

let the four no be a-3d,a-d,a+d,a+3d.

a-3d+a-d+a+d+a+3d=24 (given)

4a=24

a=6.

(a-3d)²+(a-d)²+(a+d)²+(a+3d)²=164 (given)

2(a²+9d²)+2(a²+d²)=164. since (a+b)²+(a-b)²=2(a²+b²)

2(2a²+10d²)=164.

2a²+10d²=164/2=82.

2(6)²+10d²=82.

10d²=10.

d=±1.

therefore four numbers are 3,5,7,9