((a^4)/(2a^2-4a^4))*((8a^3+1)/(2a+4a^2))

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Solution for ((a^4)/(2a^2-4a^4))*((8a^3+1)/(2a+4a^2)) equation:


D( a )

4*a^2+2*a = 0

2*a^2-(4*a^4) = 0

4*a^2+2*a = 0

4*a^2+2*a = 0

4*a^2+2*a = 0

DELTA = 2^2-(0*4*4)

DELTA = 4

DELTA > 0

a = (4^(1/2)-2)/(2*4) or a = (-4^(1/2)-2)/(2*4)

a = 0 or a = -1/2

2*a^2-(4*a^4) = 0

2*a^2-(4*a^4) = 0

2*a^2-4*a^4 = 0

t_1 = a^2

2*t_1^1-4*t_1^2 = 0

2*t_1-4*t_1^2 = 0

DELTA = 2^2-(-4*0*4)

DELTA = 4

DELTA > 0

t_1 = (4^(1/2)-2)/(-4*2) or t_1 = (-4^(1/2)-2)/(-4*2)

t_1 = 0 or t_1 = 1/2

t_1 = 0

a^2+0 = 0

a^2 = 0

1*a^2 = 0 // : 1

a^2 = 0

a = 0

t_1 = 1/2

a^2-1/2 = 0

1*a^2 = 1/2 // : 1

a^2 = 1/2

a^2 = 1/2 // ^ 1/2

abs(a) = (1/2)^(1/2)

a = (1/2)^(1/2) or a = -(1/2)^(1/2)

a in (-oo:-(1/2)^(1/2)) U (-(1/2)^(1/2):-1/2) U (-1/2:0) U (0:(1/2)^(1/2)) U ((1/2)^(1/2):+oo)

((a^4)/(2*a^2-(4*a^4)))*((8*a^3+1)/(4*a^2+2*a)) = 0

((a^4)/(2*a^2-4*a^4))*((8*a^3+1)/(4*a^2+2*a)) = 0

(a^4*(8*a^3+1))/((2*a^2-4*a^4)*(4*a^2+2*a)) = 0

2*a^2-4*a^4 = 0

2*a^2*(1-2*a^2) = 0

-2*a^2 = -1 // : -2

a^2 = 1/2

a^2 = 1/2 // ^ 1/2

abs(a) = (1/2)^(1/2)

a = (1/2)^(1/2) or a = -(1/2)^(1/2)

2*a^2*(a-(1/2)^(1/2))*(a+(1/2)^(1/2)) = 0

4*a^2+2*a = 0

2*a*(2*a+1) = 0

2*a+1 = 0 // - 1

2*a = -1 // : 2

a = -1/2

2*a*(a+1/2) = 0

(a^4*(8*a^3+1))/(2*2*a*a^2*(a-(1/2)^(1/2))*(a+(1/2)^(1/2))*(a+1/2)) = 0

( 8*a^3+1 )

8*a^3 = -1 // : 8

a^3 = -1/8

a^3 = -1/8 // ^ 1/3

a = -1/2

( a^4 )

1*a^4 = 0 // : 1

a^4 = 0

a = 0

a in { -1/2}

a in { 0}

a belongs to the empty set

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