SOLUTION: Find two integers whose sum is 96 and whose product is 1728.

Question 51433: Find two integers whose sum is 96 and whose product is 1728.
Answer by rchill(405) (Show Source): You can put this solution on YOUR website!
Let x and y represent the two integers. We now have equations and . Using the second equation, let's solve for y by dividing both sides by x: , which simplifies to . Now use this value of y and substitute it into the first equation thusly: . Multiplying both sides by x produces . Now subtract 96x from both sides to yield . Now we just have to factor this equation into (x - something) and (x - something_else), where the 'something' and 'something_else' when multiplied together produces 1728, and when added together they produce -96.

The best way to do this is not by trial and error, but by using the discriminant.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=2304 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 72, 24. Here's your graph:

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