1) \(\left(x+3\right)\left(x+5\right)\left(x+7\right)\left(x+9\right)+2033\)
\(=\left(x^2+12x+27\right)\left(x^2+12x+35\right)+2033\)
Đặt \(x^2+12x+26=t=>t^2+2t-15+2033=t\left(t+2\right)+2008\)
\(=>\left(x+3\right)\left(x+5\right)\left(x+7\right)\left(x+9\right)+2033\)
\(=\left(x^2+12x+36\right)\left(x^2+12x+30\right)+2018\) chia cho \(x^2+12x+30\) là \(2018\)
2) \(x+y+z=7=>z=-x-y+7\)
\(=>xy+z-6=xy-x-y+1=\left(x-1\right)\left(y-1\right)\)
\(=>H=\dfrac{1}{\left(x-1\right)\left(y-1\right)}+\dfrac{1}{\left(y-1\right)\left(z-1\right)}+\dfrac{1}{\left(z-1\right)\left(x-1\right)}\)
\(=\dfrac{4}{9-\left(xy+yz+xz\right)}\)
Ta có \(\left(xy+2\right)^2=x^2y^2+2^2+2\left(xy+yz+xz\right)=>xy+yz+xz=13\)
\(=>H=\dfrac{4}{9-13}=-1\)
