QQuestionMathematics
QuestionMathematics
What two numbers multiply to equal 12 but add together to equal 3?
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Answer
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Step 1:I'll solve this step by step using the specified LaTeX formatting guidelines:
Step 2:: Understand the Problem
- Add together to give $$3
We need to find two numbers that:
Step 3:: Set Up Algebraic Equations
- $$x + y = 3
We can create two equations:
Step 4:: Rearrange the Second Equation
From $$x + y = 3$$, we can express $$y$$ in terms of $$x$$:
y = 3 - x
Step 5:: Substitute into First Equation
Substituting $$y = 3 - x$$ into $$x \times y = 12$$:
x \times (3 - x) = 12
Step 6:: Expand the Equation
3x - x^{2} = 12
Step 7:: Rearrange to Standard Quadratic Form
x^{2} - 3x + 12 = 0
Step 8:: Solve Using Quadratic Formula
x = \frac{3 \pm \sqrt{-39}}{2}
Where a = 1, b = - 3, c = 12
Step 9:: Interpret Results
Since we have an imaginary number, we need to use the other method: trial and error.
Step 10:: Find the Numbers
- $$4 + (-1) = 3$$ (this works!)
By trying different combinations, we find:
Final Answer
The two numbers are 4 and - 1, which multiply to 12 and add to 3.
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