Sagot :
SOLUTION:
Let: (x), (x + 1), and (x + 2) be the three consecutive positive integers.
Formulate an equation for the problem.
- x² + (x + 1)² + (x + 2)² = 149
Solve for x.
- x² + (x + 1)² + (x + 2)² = 149
- x² + x² + 2x + 1 + x² + 4x + 4 = 149
- 3x² + 6x + 5 = 149
- 3x² + 6x - 144 = 0
- x² + 2x - 48 = 0
- (x + 8)(x - 6) = 0
- x + 8 = 0 x - 6 = 0
- x = -8 x = 6
- Take the positive root since we're looking for positive integers.
- Therefore, the first integer is 6.
Now, to find the second and third integers, substitute the value of x.
- x + 1 = 6 + 1 = 7
- The second integer is 7.
- x + 2 = 6 + 2 = 8
- The third integer is 8.
ANSWER:
- The three consecutive positive integers are 6, 7, and 8.