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

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

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

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

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solve for

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

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

Solution steps

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

Write in the standard form

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

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

Solve with the quadratic formula

x_{1, 2} = \frac{- y \pm y ^{2} - 4 \cdot 1 \cdot y ^{2}}{2 \cdot 1}

Simplify

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

x_{1, 2} = \frac{- y \pm 3 i y}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- y + 3 i y}{2 \cdot 1}, x_{2} = \frac{- y - 3 i y}{2 \cdot 1}

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

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

The solutions to the quadratic equation are:

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

s (s - 3) = 0

3 x^{2} - 46 x + 120 = 0

20 x^{2} + 5 x = 0

0 = 3 x^{2} + 2 x - 5

0 = 3 x^{2} + 2 x + 4

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