What two 2 numbers mutiplied equal 9 and when added equal 3?

Answer 1

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