Question

Find two positive numbers whose difference is 5 and whose product is 864.Answer How to enter your answer (opens in new window) 5 Pointsandev

Answer 1

For this problem, we need to find two positive numbers whose difference is 5 and the product is 864.

We will call the numbers: x and y. So we can write the following expressions:

`\begin{gathered} x-y=5\\ \\ x\cdot y=864 \end{gathered}`

We can rewrite the first expression as:

`x=5+y`

Then we can replace the expression above with the second one:

`\begin{gathered} (5+y)\cdot y=864\\ \\ y^2+5y-864=0\\ \\ \\ \end{gathered}`

We can solve the expression above to determine one of the numbers.

`\begin{gathered} y_(1,2)=(-5\pm√((5)^2-4\cdot1\cdot(-864)))/(2)\\ \\ y_(1,2)=(-5\pm√(3481))/(2)\\ \\ y_(1,2)=(-5\pm59)/(2)\\ \\ y_1=(-5+59)/(2)=27\\ \\ y_2=(-5-59)/(2)=-32 \end{gathered}`

The only possible value we can use is "27". We can find the other number by replacing "y" on the first expression with 27. We have:

`x=5+27=32`

The numbers are 27 and 32.