Question

three numbers are in AP their sum is 24 and sum of their square is 200 find the numbers ​

Answer 1

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Let the three numbers be a-d,a,a+d.

Now it is given that their sum is 24,

a-d+a+a+d=24

3a=24

a=8

Also, the sum of their squares is 200,

(a-d)²+(a)²+(a+d)²=200

a²+d²-2ad+a²+a²+d²+2ad=200

3a²+2d²=200

substituting a=8,

3(8)²+2d²=200

192+2d²=200

2d²=200-192

2d²=8

d²=4

d=2

Therefore, the 3 numbers are

a-d=8-2= 6

a=8

a+d=10

Answer: 6,8,10