You can put this solution on YOUR website!
Does anyone know how to go about this problem? The difference of two positive numbers is 3 and the sum of their squares is 65. Find the numbers.
Step 1. Let y be one positive and the larger number and x be the other positive and smaller number.
Step 2. The problem statement provides the following relationships or equations:
Step 3. Substitute (A) into (B)
Step 4. Subtract 65 from both sides of equation.
Step 5. We can use the quadratic formula given as
where a=1, b=3, and c=-28
|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=121 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 4, -7.
Here's your graph:
Step 6. Based on the above steps, select 4 since we want a positive number.
With x=4, then y=3+4=7.
which is a true statement.
Step 7. ANSWER: The numbers are 4 and 7.
I hope the above steps were helpful.
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