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

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

Grade:11

2 Answers

Kaushik
28 Points
8 years ago

they are 3,5,7,9

srinivas aytha
13 Points
8 years ago

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

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