Question

The sum of the squares of three consecutive odd numbers is 2531. Find the numbers.​

Answer 1

Answer:

27, 29, 31 or -27, -29, -31

Step-by-step explanation:

Let the numbers be x, x+2, x+4 (as they are odd so they have a difference of 2)

According to condition,

x²+(x+2)²+(x+4)²=2531

x²+x²+4+2×x×2+x²+16+2×x×4=2531  (as a+b = a²+b²+2ab)

3x²+ 12x + 20 = 2531

3x² + 12x - 2511 = 0

dividing by 3

x² + 4x - 837 = 0

This is a quadratic equation

using middle term splitting

x² + 31x - 27x - 837 = 0

x (x + 31) - 27 (x + 31) = 0

(x-27) (x+31) = 0

x - 27 = 0

x= 27

x+2=29

x+4=31

Or

x+ 31 = 0

x = -31

x + 2 = -29

x + 4 = -27

Either way, answers are correct as squares are same