- #1

chwala

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- Homework Statement
- See attached.

- Relevant Equations
- Simultaneous equations

##\dfrac{x^2}{y}+ y =2.5x##

and we know that

##2y^2=9-x^2##

##y^2=\dfrac{9-x^2}{2}##

##(\dfrac{x^2}{y}+ y)(\dfrac{x^2}{y}+ y)=(2.5x)^2##

##\dfrac{x^4}{y^2} + x^2+x^2+y^2=6.25x^2##

##\dfrac{x^4}{y^2}+2x^2+\dfrac{9-x^2}{2}=6.25x^2##

##\dfrac{2x^4}{9-x^2} +2x^2+\dfrac{9-x^2}{2}=6.25x^2##

##4x^4+2x^2(18-2x^2)+(9-x^2)^2=6.25x^2(18-2x^2)##

...

##36x^2+81-18x^2+x^4=112x^2-12.5x^4##

##12.5x^4+x^4-94.5x^2+81=0##

##13.5x^4-94.5x^2+81=0##

##x_1=6## We cannot have ##y## values for ##x_1=6##

and for ##x_2=1 ⇒y= ±2##

There should be a better approach...will explore later.