# Simultaneous equations

1. Sep 8, 2011

### rollcast

1. The problem statement, all variables and given/known data
2 positive numbers , x and y, are such that the sum of their squares is 10 times their sum.

a. write an equation to link x and y
b. If y is the larger number and the difference is 6 show that x satisfies the equation
x2-4x-12=0
c. solve the equation and fin the 2 positive numbers x and y

2. Relevant equations

3. The attempt at a solution
Part a. This is where I think I may be wrong

10x+10y=x2+y2

Part b. y= x+6, substitute in above formula, but I can't get the same quadratic equation as the question.

Part c. I can do this ok.

2. Sep 8, 2011

### Staff: Mentor

Check your math then. Or show it, so that someone can help checking.

3. Sep 8, 2011

### rollcast

So then after substituting

10x+10x+60=x^2+(x+6)^2

work that all out and collect the terms

20x+60=4x^2+36+24x

then set the equation equal to zero

4x^2-4x-24=0

divide by 4

x^2-x-6=0

But thats not what it says to show in the question

4. Sep 8, 2011

### Staff: Mentor

You right side is off, what is $(a+b)^2$ equal to?

5. Sep 8, 2011

a^2+2ab+b^2

6. Sep 8, 2011

### rollcast

seen it now, thanks

7. Sep 8, 2011

### Staff: Mentor

And $(x+6)^2$?

And $x^2+(x+6)^2$?

Edit: OK, I guess you found the problem

8. Sep 8, 2011

x^2+12x+36

2x^2 +12x+36