Question

The sum of three numbers in AP is 27 and the sum of their square is 293. Find the number.

Answer 1

let the three number be a-d, a and a+d,

then
according to the question, we have

a-d + a + a+d=27,

3a=27,

a=9,

also

(a-d)²+a²+(a+d)²=293,

(9-d)²+9²+(9+d)²=293,

(81+d²-18d) + 81 + (81+d²+18d) =293,

81+81+81+2d²=293,

243+2d²=293,

then

2d²=293-243,

2d²=50,

d²=25,

then

d=√25,

d=5,


therefore

1st number=a-d=9-5=4,

2nd number=9,

3rd number=9+5=14