Ln(4x-1)*√(x²-6x+6x+a²)=0
4x-1>0⇒4x>1⇒x>0,25
ln(4x-1)>0 при x∈(0,25;∞)
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x²-6x+6a+a²=0
D=36-24a-4a²
36-24a-4a²=0
a²+6a-9=0
D=36+36=72
√D=6√2
a1=(-6-6√2)/2=-3-3√2
a2=-3+3√2
x²-6x+a(6+a)=0
1)a=-3-3√2
x²-6x-(3+3√2)(6-3-3√2)=0
x²-6x-(3+3√2)(3-3√2)=0
x²-6x+9=0
(x-3)²=0
x-3=0
x=3
2)x²-6x+(-3+3√2)(6-3+3√2)=0
x²-6x+(-3+3√2)(3+3√2)=0
x²-6x+9=0
x=3