find the numbers. show work

Question

One number is 6 less than another. The product of the numbers is 72. Find the numbers. show all work. 

Answer 1

This will use a series of strategies to manipulate values & variables to yield the solution.

1. There is one variable - let's call it x;

2. One value is 6 less than the other. They are x & x-6;

3. The product of the two is 72, so: x(x-6)=72

4. X^2-6x=72

x^2-6x-72=0 (subtract 72 from each side);

(x-12)(x+6)=0

5. If x-12=0, then x=12;

If x+6=0, then x=-6;

Since x=-6 is impossible, we assume x=12.

6. Check the solution:

X=12, x-6=6, 12*6=72

Answer 2

X - 6 = Y

 X y = 72

 

  X = Y +6

 

 ( Y+6 ) Y = Y^2 +6Y

 

 Y^2 + 6Y = 72

 

 Y^2 + 6Y - 72 =0

 

 ( Y +12 ) ( Y -6 ) =0

 

 Y = -12  Y = 6 

 

  From the property of the quadratic equation, you should know that

 

    Roots of the following equation are two numbers 

 

 That their Sum = -6 and the product is 72

 

   Y^2 + 6Y + 72