Question

the sum of three numbers in an ap is 15 and sum of their squares is 147 find them

Answer 1

Hi friend, Harish here.

Here is your answer:

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

Given that :

Sum of the three numbers = 15

⇒ (a - d) + (a) + (a + d) = 15

⇒ 3a = 15

⇒ a = 5.

Now,

Sum of their squares = 147

⇒ ( a - d )² + (a)² + ( a + d)² = 147

⇒ ( a² + d² - 2ad ) + (a²) + (a² + d² + 2ad ) = 147

⇒ 3a² + 2d² = 147 .

[ Substitute the value of "a" that we got above ]

⇒ 3(5)² + 2d² = 147

⇒ 75 + 2d² = 147

⇒ 2d² = ( 147 - 75 ) = 72

⇒ d² = 36

⇒ d² = 6²

⇒ d = ± 6

Therefore the three numbers in AP are:

( a - d) = 5 - 6 = -1

a = 5

(a + d ) = 5 + 6 = 11

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Hope my answer is helpful to you.