Question

sum of three numbers in AP is 15 and sum of the squares of its first and third term is 58 find the number

Answer 1

let the no be a-d , a , a+d
a-d+a+a+d=15
or, 3a=15
or, a=5
(a-d)^2+(a+d)^2=58
or, a^2+ d^2-2ad+a^2+d^2+2ad=58
or, 2a^2+2d^2=58
or, 2(a^2+d^2)=58
or, 5^2+d^2=29
or, d^2=29-10
or, d=√10
so no be. 5-√10 5. 5+√10