CramX Logo

Q
QuestionMathematics

What two numbers multiply to equal 12 but add together to equal 3?
12 months agoReport content

Answer

Full Solution Locked

Sign in to view the complete step-by-step solution and unlock all study resources.

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.