Math Problem Statement
two consecutive odd numbers are such that their product is 35.find the numbers
Solution
Let's define the two consecutive odd numbers as and , where is the first odd number, and is the next consecutive odd number.
We are given that their product is 35, so we can set up the equation:
Now, expand the left side:
Next, subtract 35 from both sides to set the equation to 0:
Now, we can solve this quadratic equation. We can either use factoring, completing the square, or the quadratic formula. Let's try factoring:
We need two numbers that multiply to and add up to . These numbers are and . So, we can factor the equation as:
Now, set each factor equal to 0:
Solving these gives:
Thus, the two possible pairs of consecutive odd numbers are:
- If , the numbers are and .
- If , the numbers are and .
Conclusion:
The two consecutive odd numbers are either and , or and .
Would you like further clarification or details on this process?
Here are 5 related questions:
- How do you solve a quadratic equation using the quadratic formula?
- What are other methods for solving quadratic equations besides factoring?
- How do you determine if a number is odd or even?
- What is the significance of factoring when solving quadratic equations?
- How do you verify the solutions to quadratic equations?
Tip: When solving quadratic equations, always check the factored form to make sure both roots satisfy the original equation!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Formulas
Quadratic equation formula ax^2 + bx + c = 0
Theorems
Factoring quadratic equations
Suitable Grade Level
Grades 7-9
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