Question

Find the 2 numbers. Write your answer like this: 4,9 The product of two positive numbers is 65. One number is 3 more than two times the smaller number.

Answer 1

Let the smaller number be x

Then,

`\begin{gathered} 2x+3=y \\ \text{and} \\ xy=65 \end{gathered}`

Substitute 2x+3 for y in xy=65.

`\begin{gathered} x(2x+3)=65 \\ 2x^2+3x=65 \end{gathered}`

So this forms a qudratic equation,

`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a) \\ \text{ =}\frac{\text{-3}\pm√(9-4*2*(-65))}{2*2} \\ \text{ =-3}\pm(√(529))/(4) \\ \text{ =}\frac{\text{-3}\pm23}{4} \\ =5 \end{gathered}`

So the smallest number is 5. And

`y=2*5+3=13`

The answer is (13,5)