Решите уравнение.

a) lg^2x 2lgx-8=0

b) log3 (x^2-9x+1) = 0

1) lgx=a, x>0

a²-2a-8=0

a1+a2=2 U a1*a2=-8

a1=-2⇒lgx=-2⇒x=0,01

a2=4⇒lgx=4⇒x=10000

2) x²-9x+1>0

D=81-4=77

x1 = (9-√77) / 2 U x2 = (9+√77) / 2

x∈ (-∞; (9-√77) / 2) U ((9+√77) / 2; ∞)

x²-9x+1=1

x (x-9) = 0

x=0 U x=9