Solving Simultaneous Equations with Positive Numbers

[rollcast]

Homework Statement

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

Homework Equations

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.

 

[Borek]

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

 

[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 that's not what it says to show in the question

 

[Borek]

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

 

[rollcast]

a^2+2ab+b^2

 

[rollcast]

seen it now, thanks

 

[Borek]

And $(x+6)^2$?

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

Edit: OK, I guess you found the problem

 

[rollcast]

x^2+12x+36

2x^2 +12x+36