Question

Need Help! ASAP!!! I gave a screen shot. Please someone give me the correct answer.

Answer 1

9514 1404 393

Answer:

x ∈ {-35, 0, 35}

Explanation:

We can solve for x and equate those values to find corresponding y-values. Substituting into the original expressions for x gives the possible x-values.

`x+xy^2=250y\ \Rightarrow\ x=(250y)/(1+y^2)\\\\x-xy^2=-240y\ \Rightarrow\ x=(-240y)/(1-y^2)\\\\(250y)/(1+y^2)+(240y)/(1-y^2)=0\\\\(25y(1-y^2)+24y(1+y^2))/((1+y^2)(1-y^2))=0\\\\y(-y^2+49)=0=y(7-y)(7+y)\ \Rightarrow\ y\in\{-7,0,7\}\\\\x=(250(\pm 7))/(1+(\pm7)^2)=\pm35,\quad=(250(0))/(1+0^2)=0\\\\\boxed{x\in\{-35,0,35\}}`