Question

Find two numbers such that their sum is 12 and their product is 29​

Answer 1

Answer:

Let X = the first number

Let Y = the second number

 

Set up 2 distinct equations, based upon the above information:

 

X + Y = 12

X * Y = 34

 

Solve the 2nd equation by X, by dividing out both sides by "Y", to get:

 

X = 34/Y

 

Now, go back to the first equation, substituting in the X-Value of 34/Y into it:

 

34/Y + Y = 12

 

Next, multiply out everything by "Y", to get:

 

34 + Y2 = 12Y

 

Then, subtract 12Y from both sides, to get:

 

Y2 - 12Y + 34 = 0

 

From here, use Completing The Square, to get the X-Values.  Plug those X-values into the equations, in order to confirm the correctly corresponding Y-value(s)