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

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

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

The zeros of solvefor y,x^2+y^2=2xy are y=x

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solve for

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

y = x

Solution steps

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

Move

2 x y

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

(- 2 x)^{2} - 4 \cdot 1 \cdot x^{2} = 0

y_{1, 2} = \frac{- ( - 2 x ) \pm 0}{2 \cdot 1}

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

Simplify

\frac{- ( - 2 x )}{2 \cdot 1} : x

y = x

The solution to the quadratic equation is:

y = x

5 x - 17 = (x + 3) (x - 3)

9 x = 4 - 2 x^{2}

3 m^{2} - 16 m - 2 = - 7

3 x^{2} - x^{2} = 1800

x^{2} - 16 x - 2 = 0

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