Polynomial equation

[juandiaz]

 

[Otis]

Find 10x-2y if {x,y} are Real numbers and
5x^2 - 2xy + 2y^2 - 2x - 2y + 1 = 0

Hi juandiaz. Your approach (treating y as a constant and using the Discriminant) looks good, and following it through to the end leads to a nice Integer answer.

What do you get for 10x-2y?



[imath]\;[/imath]

 

[juandiaz]

Hi juandiaz. Your approach (treating y as a constant and using the Discriminant) looks good, and following it through to the end leads to a nice Integer answer.

What do you get for 10x-2y?



[imath]\;[/imath]

 

[juandiaz]

I’m not sure Please suggest me better solution.

 

[juandiaz]

I’ve done. Grouping polynomial

 

[Otis]

I’m not sure [about my] solution.

I got the same answer. Looks good!



[imath]\;[/imath]

 

[lex]

[imath]((5x-y)-1)^2+(3y-2)^2=0\\ \Rightarrow 10x-2y=2[/imath]