Understanding Integer Properties and Constraints

The video tutorial explores a mathematical problem involving two positive integers that differ by 60. The sum of their square roots equals the square root of a non-perfect square integer. The goal is to find the maximum possible sum of these integers. The instructor breaks down the problem, derives necessary equations, and tests various factors of 900 to find the solution. The maximum sum is determined to be 156, with integers 108 and 48 meeting all conditions.

What is the difference between the two integers in the problem?

• 70

• 50

• 60

• 80

What must be true about the product of the two integers?

• It must be a multiple of 10

• It must be a prime number

• It must be a perfect square

• It must be an even number

What mathematical technique is used to simplify the equation involving b?

• Integration

• Differentiation

• Completing the square

• Matrix multiplication

What is the significance of the number 900 in the problem?

• It is the difference between the integers

• It is the sum of the integers

• It is the product of the integers

• It is a factor used to find integer pairs

Why was the pair (196, 256) rejected as a solution?

• The sum was too high

• The product was not a perfect square

• The difference was incorrect

• The square root of c was an integer

What is the maximum possible sum of the two integers?

• 156

• 148

• 164

• 172

What is the value of b in the final solution?

• 108

• 48

• 96

• 196

What is the value of a in the final solution?

• 148

• 128

• 108

• 168

What is the square root of c in the final solution?

• 10√3

• 16√3

• 14√3

• 12√3

What is the integer value of c in the final solution?

• 200

• 300

• 250

• 350