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

## 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