Question

The sum of three numbers in A.P is 24 and the sum of their squares is 194. Find the numbers​

Answer 1

Answer:

7,8,9

Step-by-step explanation:

Square of 7 = 49, 8 = 64, 9 = 81

So, 49 + 64 + 81

= 194

Answer 2

Solution:

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

a - d, a, a + d are in AP with common difference d.

Given

Sum of numbers is 24

⇒(a - d) + a + ( a + d) = 24

⇒3a = 24

⇒ a = 8.

Sum of squares of the numbers is 194

⇒(a - d)² + a²+ ( a + d)² = 194

We have found that, a = 8

⇒(8 - d)² + 8²+ ( 8 + d)² = 194

⇒64 + d² - 16d + 64 + 64 + d² + 16d = 194

⇒(64 + 64 + 64) + 2d² + ( 16 d - 16d) = 194

⇒192 + 2d² = 194

⇒ 2d² = 194 - 192

⇒ 2d² = 2

⇒d² = 1

Either we take d = 1, - 1 doesn't matter as we have a - d and a + d.

Therefore, The numbers are 7, 8, 9.