Answer:
10, 11, 12, 13, 14
Step-by-step explanation:
Let x represent the first of these 5 consecutive whole numbers.
The next four numbers are x+1, x+2, x+3 and x+4.
Then:
x^2 + (x+1)^2 + (x+2)^2 = (x+3)^2 + (x+4)^2
Expanding this, we get:
x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = (x^2 + 6x + 9 + x^2 + 8x + 16
There are 3 x^2 terms on the left side and 2 x^2 terms on the right side. Cancel out all of these but for the first x^2 term, on the left, obtaining:
x^2 + 2x + 1 + 4x + 4 = 6x + 9 + 8x + 16. Combining like terms, we get:
x^2 + 6x + 5 = 14x + 25.
Subtracting 14x + 25 from both sides, we get:
x^2 - 8x - 20 = 0, which factors as follows:
(x - 10)(x + 2) = 0, whose roots are 10 and -2.
Focusing on positive consecutive numbers, we start with x = 10 and continue: 10, 11, 12, 13, 14.
It remains to be shown that another solution is:
-2, -1, 0, 1, 2
