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

The solutions to the equation solvefor x,x^2+xy=y^2 are x=(-y+sqrt(5)y)/2 ,x=(-y-sqrt(5)y)/2

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

The zeros of solvefor x,x^2+xy=y^2 are x=(-y+sqrt(5)y)/2 ,x=(-y-sqrt(5)y)/2

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solve for

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

x = \frac{- y + 5 y}{2}, x = \frac{- y - 5 y}{2}

Solution steps

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

Move

y^{2}

to the left side

x^{2} + x y - y^{2} = 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}) : 5 y

x_{1, 2} = \frac{- y \pm 5 y}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- y + 5 y}{2 \cdot 1}, x_{2} = \frac{- y - 5 y}{2 \cdot 1}

x = \frac{- y + 5 y}{2 \cdot 1} : \frac{- y + 5 y}{2}

x = \frac{- y - 5 y}{2 \cdot 1} : \frac{- y - 5 y}{2}

The solutions to the quadratic equation are:

x = \frac{- y + 5 y}{2}, x = \frac{- y - 5 y}{2}

3 x^{2} - 24 x - 100 = 0

39 = x^{2} - 2 x + 4

x, (x + y_{i})^{2} = 3 - 4 i

x, 4 x^{2} + 9 x + 3 = 0

2 x^{2} - 3 x + \frac{5}{8} = 0

What are the solutions to the equation solvefor x,x^2+xy=y^2 ?
The solutions to the equation solvefor x,x^2+xy=y^2 are x=(-y+sqrt(5)y)/2 ,x=(-y-sqrt(5)y)/2
Find the zeros of solvefor x,x^2+xy=y^2
The zeros of solvefor x,x^2+xy=y^2 are x=(-y+sqrt(5)y)/2 ,x=(-y-sqrt(5)y)/2