What are the solutions to the equation solvefor y,x^2+xy+y^2=0 ?

The solutions to the equation solvefor y,x^2+xy+y^2=0 are y=-x/2+i(sqrt(3)x)/2 ,y=-x/2-i(sqrt(3)x)/2

Find the zeros of solvefor y,x^2+xy+y^2=0

The zeros of solvefor y,x^2+xy+y^2=0 are y=-x/2+i(sqrt(3)x)/2 ,y=-x/2-i(sqrt(3)x)/2

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solve for

y, x^{2} + x y + y^{2} = 0

y = - \frac{x}{2} + i \frac{3 x}{2}, y = - \frac{x}{2} - i \frac{3 x}{2}

Solution steps

x^{2} + x y + y^{2} = 0

Write in the standard form

a x^{2} + b x + c = 0

y^{2} + x y + x^{2} = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- x \pm x ^{2} - 4 \cdot 1 \cdot x ^{2}}{2 \cdot 1}

Simplify

x^{2} - 4 \cdot 1 \cdot x^{2} : 3 i x

y_{1, 2} = \frac{- x \pm 3 i x}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- x + 3 i x}{2 \cdot 1}, y_{2} = \frac{- x - 3 i x}{2 \cdot 1}

y = \frac{- x + 3 i x}{2 \cdot 1} : - \frac{x}{2} + i \frac{3 x}{2}

y = \frac{- x - 3 i x}{2 \cdot 1} : - \frac{x}{2} - i \frac{3 x}{2}

The solutions to the quadratic equation are:

y = - \frac{x}{2} + i \frac{3 x}{2}, y = - \frac{x}{2} - i \frac{3 x}{2}

- b^{2} + 7 \cdot b - 10 = 0

x^{2} + 2 x + 2 = 0

x^{2} = \frac{5.6}{2.45}

x^{2} - 64 = 0

\frac{- 9 + ( x - 3 ) ^{2}}{- 4} = - 4

What are the solutions to the equation solvefor y,x^2+xy+y^2=0 ?
The solutions to the equation solvefor y,x^2+xy+y^2=0 are y=-x/2+i(sqrt(3)x)/2 ,y=-x/2-i(sqrt(3)x)/2
Find the zeros of solvefor y,x^2+xy+y^2=0
The zeros of solvefor y,x^2+xy+y^2=0 are y=-x/2+i(sqrt(3)x)/2 ,y=-x/2-i(sqrt(3)x)/2