what are the three consecutive positive integers such that the sum of their squares is 149

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.