Answer:
21, 22, 23 or
-23, -22 , -21
Explanation:
The 3 consecutive integers are x, x + 1, and x + 2
Sum of the squares of the 3 consecutive integers:
x² + (x+1)² + (x+2)² = 1454 Expand this equation
x² + x² + 2x + 1 + x² + 4x + 4 = 1454 Combine like terms
3x² + 6x + 5 = 1454
3x² + 6x + 5 - 1454= 0
3x² + 6x - 1449 = 0
Use quadratic equation to solve for the roots of x: (a = 3, b = 6,
c= -1449)
x = 21, -23
The consecutive numbers are: x, (x + 1), (x + 2)
21, 22, 23
-23, -22 , -21