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find the numbers. show work

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2 Answers

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
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