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Verified answer

3.
lg(3x²+12x+19)-lg(3x+4)=lg10
lg(3x²+12x+19)=lg10+lg(3x+4)
lg(3x²+12x+19)=lg(10*(3x+4))
3x²+12x+19=30x+40
3x²-18x-21=0   D=576
x₁=7     x₂=-1.
Ответ: x₁=7    x₂=-1.
8.
3^(1+log₃(x²+y²))=15         ОДЗ:  x-y>0   x>y
log₃(x²-y²)-log₃(x-y)=0
log₃((x-y)(x+y)/(x-y)=0    x≠y
log₃(x+y)=0
x+y=3⁰=1
y=1-x
log₃3^(1+log₃(x²+y²))=log₃15
1+log₃(x²+y²)=log₃15
log₃(x²+y²)=log₃15-1
log₃(x²+y²)=log₃15-log₃3
log₃(x²+y²)=log₃(15/3)
log₃(x²+y²)=log₃5
x²+y²=5
y=1-x  ⇒
x²+(1-x)²=5
x²+1-2x+x²=5
2x²-2x-4=0   |÷2
x²-x-2=0   D=9
x₁=2     y=1-2=-1
x₂=-1    y=1-(-1)=2  ∉  по ОДЗ (x>y)
Ответ: x=2    y=-1.