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