Question

write two numbers that multiply to the value on top and add to the value on bottom.
64
×
+
16
answer
submit answer

Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \). We know that \( x \times y = 64 \) and \( x + y = 16 \). From the second equation, we can express \( y = 16 - x \).

Step2: Substitute into product equation

Substitute \( y = 16 - x \) into \( x \times y = 64 \), we get \( x(16 - x)=64 \).

Step3: Solve the quadratic equation

Expand the left side: \( 16x - x^{2}=64 \). Rearrange to standard quadratic form: \( x^{2}-16x + 64 = 0 \). This factors as \( (x - 8)^{2}=0 \).

Step4: Find the numbers

Solving \( (x - 8)^{2}=0 \) gives \( x = 8 \). Then \( y = 16 - 8 = 8 \).

Answer:

The two numbers are 8 and 8. So the boxes should be filled with 8 and 8.