Question

11. Eight more than the square of a number is the same as six timesthe number. Find the number. (Hint: There are two possibilities.)

Answer 1

Step-by-step explanation

Given that eight more than the square of a number is the same as six times the number.

Let the number be x

Therefore

`\begin{gathered} \text{square of the number =}x^2 \\ \text{eight more than the square of the number =}x^2+8 \\ \text{six times the number =}6x \end{gathered}`

Hence, the equation is interpreted as;

`\begin{gathered} x^2+8=6x \\ x^2-6x+8=0 \end{gathered}`

We can therefore solve using the factorization method.

-4 and -2 are the numbers that would serve for the sum and products of factors.

`\begin{gathered} x^2-4x-2x-8=0 \\ x(x-4)-2(x-4)=0 \\ (x-2)(x-4)=0 \\ x=2\text{ and x=4} \\ \end{gathered}`

Answer: 2 and 4