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The product of two positive consecutive numbers is 42. What is the larger number?
Step 1. Let n be the smaller positive number.
Step 2. Let n+1 be the next consecutive and larger positive number.
Step 3. Then n(n+1)=42 since their product is 42.
Step 4. Subtract 42 from both sides of the equation to get a quadratic.
Step 5. To solve, use the quadratic equation given below as
where a=1, b=1, and c=-42
|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=169 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 6, -7.
Here's your graph:
Selecting the positive solution n=6, then n+1=7. Also note their product is 42.
Step 6. ANSWER: The larger number is 7.
I hope the above steps were helpful.
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