The sum of squares of three successive integers is 99374. Sum of these integers is?

M4maths Previous Puzzles

18 Mar 2020 Arithmetic

The sum of squares of three successive integers is 99374. Sum of these integers is?

OPtion

1) 440
2) 446
3) 646
4) 546
5) 746
6) 596
7) 576
8) 526
9) 528
10) None of these

Solution

(a-1)^2 + a^2 + (a+1)^2 = 99374
=> a^2 -2a + 1 + a^2 + a^2 + 2a + 1 = 99374
=> 3a^2 + 2 = 99374
=> a^2 = (20174-2)/3 = 33124
=> a = 182
So the 3 numbers are 181, 182 and 183 and their sum is 546

Correct Option: 4 Best Solution (3)