2/x-89/8x-2

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Solution for 2/x-89/8x-2 equation:


D( x )

x = 0

x = 0

x = 0

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

2/x-8 > (9/8)*x-2 // - (9/8)*x-2

2/x-((9/8)*x)-8+2 > 0

(-9/8)*x+2/x-8+2 > 0

(-9/8)*x+2/x-8+2 = 0

2*x^-1-9/8*x^1-6*x^0 = 0

(2*x^0-9/8*x^2-6*x^1)/(x^1) = 0 // * x^2

x^1*(2*x^0-9/8*x^2-6*x^1) = 0

x^1

(-9/8)*x^2-6*x+2 = 0

(-9/8)*x^2-6*x+2 = 0

DELTA = (-6)^2-(2*4*(-9/8))

DELTA = 45

DELTA > 0

x = (45^(1/2)+6)/(2*(-9/8)) or x = (6-45^(1/2))/(2*(-9/8))

x = -4/9*(3*5^(1/2)+6) or x = -4/9*(6-3*5^(1/2))

x in { -4/9*(3*5^(1/2)+6), -4/9*(6-3*5^(1/2))}

(x+4/9*(3*5^(1/2)+6))*(x+4/9*(6-3*5^(1/2))) > 0

(-oo:-4/9*(3*5^(1/2)+6)) (-4/9*(3*5^(1/2)+6):-4/9*(6-3*5^(1/2))) (-4/9*(6-3*5^(1/2)):+oo) x+4/9*(3*5^(1/2)+6) - + + x+4/9*(6-3*5^(1/2)) - - +

x in (-oo:-4/9*(3*5^(1/2)+6)) U (-4/9*(6-3*5^(1/2)):+oo)

(-oo:-4/9*(3*5^(1/2)+6)) U (-4/9*(6-3*5^(1/2)):+oo)

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