- #1

chwala

Gold Member

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- Homework Statement
- ##\dfrac{x+2}{y-4} +\dfrac{2(y-4)}{x+2} + 3=0##

##x-y=3##

- Relevant Equations
- knowledge of simultaneous equations

##\dfrac{x+2}{y-4} +\dfrac{2(y-4)}{x+2} + 3=0##

##x-y=3##

My approach, will call it brute force, i have

##y=x-3##

then,

##\dfrac{(x+2)^2+2(y-4)^2}{(x+2)(y-4)}=-3##

##(x+2)^2+2(y-4)^2=-3(x+2)(y-4)##

##(x+2)^2+2(x-7)^2=-3(x+2)(x-7)##

##x^2+4x+4+2(x^2-14x+49)+3(x^2-5x-14)=0##

##6x^2-39x+60=0##

##x_1=4, y_1=1## and ##x_2=2.5, y_2=-0.5##

there could be a much better and simpler approach that prompted my post.

cheers man!

##x-y=3##

My approach, will call it brute force, i have

##y=x-3##

then,

##\dfrac{(x+2)^2+2(y-4)^2}{(x+2)(y-4)}=-3##

##(x+2)^2+2(y-4)^2=-3(x+2)(y-4)##

##(x+2)^2+2(x-7)^2=-3(x+2)(x-7)##

##x^2+4x+4+2(x^2-14x+49)+3(x^2-5x-14)=0##

##6x^2-39x+60=0##

##x_1=4, y_1=1## and ##x_2=2.5, y_2=-0.5##

there could be a much better and simpler approach that prompted my post.

cheers man!