Question

Decide!!!!!!!!!!!!!!!!!!!

Answer 1

• n = {9, 10}

Explanation:

Let the equation be:

• n² - 19n + 91 = k²

Multiply both sides by 4 and complete the square:

• 4n² - 76n + 364 = 4k²
• (2n)² - 2(2n)(19) + 19² + 3 = 4k²
• (2n - 19)² - 4k² = - 3
• (2n + 2k - 19)(2n - 2k - 19) = -3

Since -3 = 1(-3) = (-1)*3, we have following options:

1)

• 2n + 2k - 19 = 1
• 2n - 2k - 19 = -3

Eliminate k by adding up equations:

• 4n - 38 = -2
• 4n = 36
• n = 9

2)

• 2n + 2k - 19 = -1
• 2n - 2k - 19 = 3

Eliminate k by adding up equations:

• 4n - 38 = 2
• 4n = 40
• n = 10