Question

The product of two consecutive integers is 182. What are the two integers?A certain number added to its square is 20. What is the number?

Answer 1

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

In this case, let the consecutive integers be x and x+1.

`\begin{gathered} \text{Their product is 182, thus we have:} \\ x(x+1)=182 \\ x^2+x=182 \\ x^2+x-182=0 \\ By\text{ factorisation method, we have:} \\ (x^2+14x)-(13x-182)=0 \\ x(x+14)-13(x+14)=0 \\ (x+14)(x-13)=0 \\ x+14=0\text{ OR x-13=0} \\ x=-14\text{ or 13} \end{gathered}`
`\begin{gathered} When\text{ x=-14,} \\ \text{the consecutive integers x and x+1 becomes -14 and -14+1, which is equal to -14 and 13} \\ \text{The product of -14 and 13 is -182} \end{gathered}`
`\begin{gathered} \text{When x=13,} \\ \text{the consecutive integers x and x+1 becomes 13 and 13+1, which is 13 and 14} \\ \text{The product of 13 and 14 is 182} \end{gathered}`

Hence, the two(2) consecutive integers are 13 and 14.