Question

The second number is four more than the first number. If square of smaller number is 2 less than 3 times the larger number what are numbers

Answer 1

The numbers are 5 and 9 or -2 and 2

Step-by-step explanation

Let the first number be represented as y

The second number is four more than the first number implies 4 + y

The square of the smaller number is y²

3 times the larger number is 3(4 + y) = 12 + 3y

The square of the smaller number is 2 less than 3 times the larger number implies

`\begin{gathered} (12+3y)-y^2=2 \\ -y^2+3y+12=2 \\ -y^2+3y+12-2=0 \\ -y^2+3y+10=0 \\ \text{Multiply all through by -1} \\ y^2-3y-10=0 \end{gathered}`

Using the factorization method of solving quadratic equation, the equation becomes

`\begin{gathered} y^2-3y-10=0 \\ y^2-5y+2y-10=0 \\ y(y-5)+2(y-5)=0 \\ (y-5)(y+2)=0 \\ \text{Either }y-5=0\text{ or }y+2=0 \\ y=5,\text{ or -2} \end{gathered}`

This means the first number is 5, or -2

To get the second number, recall that the second number = 4 + y

When y = 5

The second number is 4 + 5 = 9

Also, when y = -2

The second number is 4 + (-2) = 2

Hence, the second number is 9 or 2

Therefore, the numbers are 5 and 9 or -2 and 2