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First, set one of the number to X and the other to Y.
Then, write out the equation: X+Y=3 , X*Y=9
On this equation: X+Y=3 , move any variable to one side(For this I will move variable X).
So Y= 3-X.
Replace 3-X in the MULTIPLICATION EQUATION.
So it becomes X*(3-X)=9
SOLVE
-X2+3X=9
Multiply both sides by "-1"
X2-3X=-9
Add 9 to both sides
X2-3X+9=0
COMPLETE THE SQUARE
X2-3X+(9/4)+9=0
Factor!!
(X-3/2)2+9=0
Subtract 9 on both sides
(X-3/2)2=-9
square root both sides
(X-3/2)=3i.................. i is called an imaginary number
Add 3/2 to both sides
X=3/2+3i So X=3/2+3i
Plug this into the easiest equation that you can use(out of the original equation: X+Y=3 , X*Y=9)
It seems like X+Y=3 is the easiest equation. Replace X to 3/2+3i
3/2+3i+Y=3
Subtract 3/2+3i on both sides
then Y= 3/2-3i
So the answer is X=3/2+3i and Y= 3/2-3i
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∙ 12y ago
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