Question

write two numbers that multiply to the value on top and add to the value on bottom.
6
×
+
5
answer attempt 1 out of 2
submit answer

Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \). We know that \( x \times y = 6 \) and \( x + y = 5 \).

Step2: Solve the system of equations

From the first equation, we can express \( y=\frac{6}{x} \). Substitute this into the second equation: \( x+\frac{6}{x}=5 \). Multiply through by \( x \) (assuming \( x
eq0 \)) to get \( x^{2}+6 = 5x \), which rearranges to \( x^{2}-5x + 6=0 \).

Step3: Factor the quadratic equation

Factor \( x^{2}-5x + 6 \). We need two numbers that multiply to 6 and add to - 5. The numbers are -2 and -3, but wait, actually for \( x^{2}-5x + 6=(x - 2)(x - 3)=0 \). So the solutions are \( x = 2 \) or \( x = 3 \). If \( x = 2 \), then \( y=3 \); if \( x = 3 \), then \( y = 2 \).

Answer:

The two numbers are 2 and 3 (or 3 and 2).