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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
3*x-((3*a-5)/x)-a-5 = 0
(-1*(3*a-5))/x-a+3*x-5 = 0
(-1*(3*a-5))/x+(-a*x)/x+(3*x*x)/x+(-5*x)/x = 0
3*x*x-1*(3*a-5)-a*x-5*x = 0
3*x^2-3*a-(a*x)-5*x+5 = 0
(3*x^2-3*a-(a*x)-5*x+5)/x = 0
(3*x^2-3*a-(a*x)-5*x+5)/x = 0 // * x
3*x^2-3*a-(a*x)-5*x+5 = 0
3*x^2-3*a-5*x+5 = 0
DELTA = (-5)^2-(3*4*(5-3*a))
DELTA = 25-12*(5-3*a)
25-12*(5-3*a) = 0
25-12*(5-3*a) = 0
36*a-35 = 0
36*a-35 = 0
36*a-35 = 0 // + 35
36*a = 35 // : 36
a = 35/36
DELTA = 0 <=> t_3 = 35/36
x = 5/(2*3) i a = 35/36
x = 5/6 i a = 35/36
( x = ((25-12*(5-3*a))^(1/2)+5)/(2*3) or x = (5-(25-12*(5-3*a))^(1/2))/(2*3) ) i a > 35/36
( x = ((25-12*(5-3*a))^(1/2)+5)/6 or x = (5-(25-12*(5-3*a))^(1/2))/6 ) i a > 35/36
a-(35/36) > 0
a-35/36 > 0
a-35/36 > 0 // + 35/36
a > 35/36
x in { 5/6, ((25-12*(5-3*a))^(1/2)+5)/6, (5-(25-12*(5-3*a))^(1/2))/6 }
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