(6x^2y^4-12x^4y^2)/(2x^2)

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Solution for (6x^2y^4-12x^4y^2)/(2x^2) equation:


D( x )

2*x^2 = 0

2*x^2 = 0

2*x^2 = 0

2*x^2 = 0 // : 2

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

(6*x^2*y^4-(12*x^4*y^2))/(2*x^2) = 0

(6*x^2*y^4-12*x^4*y^2)/(2*x^2) = 0

6*x^2*y^4-12*x^4*y^2 = 0

6*x^2*y^2*(y^2-2*x^2) = 0

-2*x^2 = -y^2 // : -2

x^2 = (y^2)/2

x^2 = (y^2)/2 // ^ 1/2

abs(x) = y/(2^(1/2))

x = y/(2^(1/2)) or x = -(y/(2^(1/2)))

6*x^2*y^2*(x-2^(-1/2)*y)*(x+(1/(2^(1/2)))*y) = 0

(6*x^2*y^2*(x-2^(-1/2)*y)*(x+(1/(2^(1/2)))*y))/(2*x^2) = 0

( 6*x^2*y^2 )

6*x^2*y^2 = 0 // : 6*y^2

x^2 = 0

x = 0

( x+(1/(2^(1/2)))*y )

x+(1/(2^(1/2)))*y = 0 // - (1/(2^(1/2)))*y

x = -((1/(2^(1/2)))*y)

x = -(y/(2^(1/2)))

( x-2^(-1/2)*y )

x-2^(-1/2)*y = 0 // + -2^(-1/2)*y

x = -(-2^(-1/2)*y)

x in { 0}

x in { -(y/(2^(1/2))), -(-2^(-1/2)*y) }

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