The sum of three numbers in A.P. is 27 and the sum of their squares is 275 . Find the numbers .

Explanation

Let the numbers be a - d , a, a + d
Now , ` (a - d) + a + (a + d) = 27 rArr 3a = 27 rArr a = 9 `
` Thus numbers are ` 9- d, 9,9 + d `
Also , ` (9 - d)^(2) + 9^(2) + (9 + d)^(2) = 275`
` rArr 81 - 18d + d^(2) + 81 + 81 + 18 d + d^(2) = 275`
` rArr 243 + 2d^(2) = 275`
` rArr 2d^(2) = 32 `
` rArr d^(2) = 16 rArr d = pm 4 `
Thus numbers are 5, 9, 13 or 13, 9 , 5