What are the solutions to the equation solvefor x,x^2+y^2=4xy ?

The solutions to the equation solvefor x,x^2+y^2=4xy are x=(2+sqrt(3))y,x=(2-sqrt(3))y

Find the zeros of solvefor x,x^2+y^2=4xy

The zeros of solvefor x,x^2+y^2=4xy are x=(2+sqrt(3))y,x=(2-sqrt(3))y

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solve for

x, x^{2} + y^{2} = 4 x y

x = (2 + 3) y, x = (2 - 3) y

Solution steps

x^{2} + y^{2} = 4 x y

Move

4 x y

to the left side

x^{2} + y^{2} - 4 x y = 0

Write in the standard form

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

x^{2} - 4 y x + y^{2} = 0

Solve with the quadratic formula

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

Simplify

(- 4 y)^{2} - 4 \cdot 1 \cdot y^{2} : 23 y

x_{1, 2} = \frac{- ( - 4 y ) \pm 2 3 y}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 4 y ) + 2 3 y}{2 \cdot 1}, x_{2} = \frac{- ( - 4 y ) - 2 3 y}{2 \cdot 1}

x = \frac{- ( - 4 y ) + 2 3 y}{2 \cdot 1} : (2 + 3) y

x = \frac{- ( - 4 y ) - 2 3 y}{2 \cdot 1} : (2 - 3) y

The solutions to the quadratic equation are:

x = (2 + 3) y, x = (2 - 3) y

3 x^{2} - 24 x + 40 = 0

x^{2} - 10 = 2 x^{2}

n^{2} + 6 n + 9 = 0

x^{2} - x - 0 = 0

(2 x - 3)^{2} - 6 = 43

What are the solutions to the equation solvefor x,x^2+y^2=4xy ?
The solutions to the equation solvefor x,x^2+y^2=4xy are x=(2+sqrt(3))y,x=(2-sqrt(3))y
Find the zeros of solvefor x,x^2+y^2=4xy
The zeros of solvefor x,x^2+y^2=4xy are x=(2+sqrt(3))y,x=(2-sqrt(3))y