Question

Three numbers in AP.have the sum 18 and tho sum of their squares is 180. Find the numbersin the increasing order.

Answer 1

Let (a - d) , d , (a + d) are three terms in an AP.
A/C to question,
sum of three terms = 18
(a - d ) + d + (a + d) = 18
3a = 18
a = 6 ..........(i)

again, A/C to question,
sum of their squares = 180
(a - d)² + d² + (a + d)² = 180
a² + d² - 2ad + d² + a² + d² + 2ad = 180
2a² + 3d² = 180
2(6)² + 3d² = 180 [ from eq. (i)
2 × 36 + 3d² = 180
3d² = 180 - 72 = 108
d² = 36
d = ± 6

for increasing order , take d = 6
so, (a - d) = 6 - 6 = 0
d = 6
and (a + d) = 6 + 6 = 12

hence increasing order : 0, 6, 12