1/(2x-1)^2=4

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Solution for 1/(2x-1)^2=4 equation:


D( x )

(2*x-1)^2 = 0

(2*x-1)^2 = 0

(2*x-1)^2 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

x in (-oo:1/2) U (1/2:+oo)

1/((2*x-1)^2) = 4 // - 4

1/((2*x-1)^2)-4 = 0

1/((2*x-1)^2)+(-4*(2*x-1)^2)/((2*x-1)^2) = 0

1-4*(2*x-1)^2 = 0

16*x-16*x^2-3 = 0

16*x-16*x^2-3 = 0

16*x-16*x^2-3 = 0

DELTA = 16^2-(-16*(-3)*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)-16)/(-16*2) or x = (-64^(1/2)-16)/(-16*2)

x = 1/4 or x = 3/4

(x-1/4)*(x-3/4) = 0

((x-1/4)*(x-3/4))/((2*x-1)^2) = 0

((x-1/4)*(x-3/4))/((2*x-1)^2) = 0 // * (2*x-1)^2

(x-1/4)*(x-3/4) = 0

( x-1/4 )

x-1/4 = 0 // + 1/4

x = 1/4

( x-3/4 )

x-3/4 = 0 // + 3/4

x = 3/4

x in { 1/4, 3/4 }

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