Question

A number is six more than one-half the other number, and the difference of their squares is 99. Find the numbers.

Applications Quadratic Equations

Answer 1

Explanation:

Let the first number = x

Let the second number = y

Equation One

x = 1/2 y + 6;

2x = y + 12

2x - 12 = y

Second Equation

x^2 - y^2 = 99 Substitute for y^2

x^2 - (2x - 12)^2 = 99

x^2 - (4x^2 - 48x + 144) = 99

x^2 - 4x^2 + 48x - 144 = 99

- 3x^2 + 48x - 144 - 99 = 0

- 3x^2 + 48x - 243 = 0 Divide by -3

x^2 - 16x + 81 = 0

Use of the quadratic formula gives

8 +/- 123i

You may not know how to get complex numbers, but that is what this one comes to.