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

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


D( x )

x < 0

x < 0

x in <0:+oo)

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

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

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

t_1 = x^(1/2)

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

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

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

DELTA = 32

DELTA > 0

t_1 = (32^(1/2)-4)/(-2*2) or t_1 = (-32^(1/2)-4)/(-2*2)

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

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

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

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

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

( (4*2^(1/2)-4)/(-4) < 0 i 1/2 in (0:1) ) => x należy do O

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

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

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

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

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

x = ((-4*2^(1/2)-4)^2)/16

x = ((-4*2^(1/2)-4)^2)/16

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