Question

Find the two postive number whose difference is 9 and whose product is 190

Answer 1

Given

find the two positive numbers whose difference is 9 and whose product is 190​

Solution

Let n and n+9 be the two numbers.

`\begin{gathered} \text{Their product } \\ n(n+9)=190 \\ n^2+9n=190 \\ n^2+9n-190=0 \end{gathered}`

It is now a quadratic equation

we can factorize

`\begin{gathered} n^2+19n-10n-190=0 \\ (n^2+19n)-(10n+190)=0 \\ \text{factorize} \\ n(n+19)-10(n+19)=0 \\ n-10=0 \\ n=10 \\ \text{and} \\ n+19=0 \\ n=-19 \end{gathered}`

The final answer is

The two positive numbers are 19 and 10