[log2(4x)*log2(4x)] + [log2(2x)*log2(2x)] =1
[log2(4)+log2(x)]^2+ [log2(2)+log2(x)]^2=1
[2+log2(x)]^2 + [1+log2(x)]^2=1
4+4log2(x)+[log2(x)]^2 + 1+2log2(x)+[log2(x)]^2-1=0
2[log2(x)]^2 +6log2(x)+4=0 |:2
[log2(x)]^2+3log2(x)+2=0
Замена: log2(x)=t
t^2+3t+2=0
D=3^2-4*1*2=1
t1=(-3-1)/2=-2
t2=(-3+1)/2=-1
Обратная замена:
1)log2(x)=-2
log2(x)=log2(1/4)
x=1/4
2)log2(x)=-1
log2(x)=log2(1/2)
x=1/2
Ответ: 1/4; 1/2