1) log12 (x^2-8x+16)=0 2) log1/2(x^2+3x-1)= - 2

Question

1) log12 (x^2-8x+16)=0
2) log1/2(x^2+3x-1)= - 2

Answer 1

1) log12(x²-8x+16)=0
log12(x²-8x+16)=log12(1)
x²-8x+16=1
x²-8x+15=0
по теореме Виетта
x1+x2=8
x1*x2=15
x1=3
x2=5
ответ: 3; 5
2) log1/2(x²+3x-1)=-2
loa1/2(x²+3x-1)=log1/2(4)
x²+3x-1=4
x²+3x-5=0
D=b²-4ac=3²-4*1*(-5)=9+20=29
x1=(-b+√D)/2a=(-3+√29)/2
x2=(-b-√D)/2a=(-3-√29)/2<0<br>ответ: (-3+√29)/2