Question

решите уравнение log2(x+4)+2log2(1/2-x)=0

Answer 1

$log_{2}(x+4)+ log_{2}( frac{1}{2}-x)^2=log_2}1$
(x+4)(0.5-x)²=1,  -4≤x≤0.5
(x+4)(0.25-x+x²)-1=0
0.25x-x²+x³+1-4x+4x²-1=0
x³+3x²+0.25x=0
x(x²+3x+0.25)=0
x1=0
D=9-1=8
x2=(-3-2√2)/2,  x3=(-3+2√2)/2