Question

log2(11-x)+ log2(x+1)=log2((x+1)x2+5x-5)
срочно

Answer 1

log₂(11-x)+log₂(x+1)=log₂((x+1)*x²+5x+5)
log₂((11-x)*(x+1)0=log₂(x³+x²+5x+5)
ОДЗ:  11-x>0 x<11  x+1>0  x>-1   x∈(-1;11)
-x²+10x+11=x³+x²+5x+5
x³+2x²-5x-6=0
(x³+x²)+(x²-5x-6)=0
x²(x+1)+(x-6)(x+1)=0
(x+1)(x²+x-6)=0
x+1=0
x₁=-1  x₁∉
x²+x-6=0   D=25
x₂=2    x₃=-3   x₃∉
Ответ:  х=2.