Question

how to solve x^2-xy-2y^2=0​

Answer 1

Answer:

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Answer 2

Answer:

If you are looking for integer solutions, then:

x2+xy+y2=0 ∖⋅2⟺ x2+y2+(x+y)2=0

⟺x=0 and y=0 and x+y=0 , so we have our only solution (x,y)=(0,0)

Next, for rationals and reals, we have:

x2+xy+y2=0 → (x+12y)2+34y2=0

⟺x+12y=0 and y=0 , again we get (x,y)=(0,0) as our only solution.

Now for the complex:

if y=0 then x=0 as well, so (x,y)=(0,0) ,

now if y≠0 , x2+xy+y2=0 ∖⋅1y2

x2y2+xy+1=0⟺xy=−1±−3√2 , which gives us two families of solutions

x=y−1+i3√2 , and x=y−1−i3√2 for arbitrary y∈C

Step-by-step explanation:

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