Question

Three numbers are in AP and their sum is 18 and sum of their squares is 140.Find the numbers

Answer 1

a + a+d + a+2d = 18

3a + 3d = 18

a + d = 6

d = 6-a

a² + (a+d)² + (a+2d)² = 140

a² + (6)² + {a+2(6-a)}² = 140

a² + 36 + (a+12-2a)² = 140

a² + 36 + (12-a)² = 140

a² + 36 + 144 - 24a + a² = 140

2a² - 24a + 40 = 0

a² - 12a + 20 = 0

a² - 2a - 10a + 20 = 0

a(a-2) - 10(a-2) = 0

(a-2) (a-10) = 0

a = 2 , 10

when , a = 2 then d = 4

So , the numbers are 2 , 6 & 10

when , a = 10 , then d = -4

So , the numbers are 10 , 6 & 2