Hard Problem, Need Help

Hi there, All that you have to do to solve the problem x^2 - 10x + y^2 - 20y Is find the value of X and Y. When finding the value of x, you count y as 0 so

x^2 - 10x + y^2 - 20y
Is really
x^2 - 10x + 0^2 - (20*0)

simplify for the x's

then do the same for the Y's



I do the work for you, but i will tell you how its done!

mathguy007:

x^2-10x+y^2-20y=-125 what is x+y=? :o
Please help, Thanks! :D

Reply ----------


X^2-10X+y^2-20y=-125
This equation is a circle.
This is the same equation in standard form:
(x-5)^2 + (y-10)^2 = -125+(5^2) + (10^2) + 125 = 0
Solving results in circle with a zero radius.
This is also known as a point singularity.
This point exists on a real number plane at coordinates (5,10).

--D--

mathguy007:

x^2-10x+y^2-20y=-125 what is x+y=?

Please help, Thanks!

David is correct in everything that he said.
I just thought I would comment because you actually didn't need to recognise all that.
You do need to complete the squares.
that is
x ²-10x +y ²-20y = -125

x ²-10x +25 +y ²-20y +100 = -125 +25+100

(x-5) ² + (y-10) ² = 0

(x-5) ² = - (y-10) ²

now the left hand side is a square so it has to be positive
the right hand side is a neg * a square so it has to be negative.
The only way that this can make any sense is if they are both 0
so x-5=0 and y-10=0
x=5, y=10

x+y = ?