Question

С.c7. The difference of two positive numbers is six. Their product is 223 less than the sum of their squares. Whatethe two numbers?

Answer 1

Let two unknow positive number is "x" and "y"

Difference of two positive number is 6 that mean:

`x-y=6`

Their product is 223 less than the sum of their square:

`\begin{gathered} x* y=x^2+y^2-223 \\ xy=x^2+y^2-223 \end{gathered}`

Substitute x with variable y:

So,

`\begin{gathered} x-y=6 \\ x=6+y \end{gathered}`

Put the value of "x" in another equation:

`\begin{gathered} xy=x^2+y^2-223 \\ (6+y)y=(6+y)^2+y^2-223 \\ 6y+y^2=36+y^2+12y+y^2-223 \\ y^2+6y-187=0 \\ y^2+17y-11y-187=0 \\ y(y+17)-11(y+17)=0 \\ (y+17)(y-11)=0 \\ y=-17;y=11 \end{gathered}`

Given number is positive that mean y=11 and so value of x is:

`\begin{gathered} x=6+y \\ x=6+11 \\ x=17 \end{gathered}`

So the number is 11 and 17.