a/ \(x^3+3x^2+3x+1+6=0\)
\(\Leftrightarrow\left(x+1\right)^3=-6\)
\(\Leftrightarrow x+1=-\sqrt[3]{6}\)
\(\Rightarrow x=-1-\sqrt[3]{6}\)
b/ \(16x^3-16x^2+4x^2+3x-7=0\)
\(\Leftrightarrow16x^2\left(x-1\right)+\left(x-1\right)\left(4x+7\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(16x^2+4x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\16x^2+4x+7=0\left(vn\right)\end{matrix}\right.\)
\(A=27x^3-54x^2+36x-8+54x^2-6+4\)
\(=27x^3+36x-10\)
\(B=8x^3+36x^2+54x+27-2x^3-12x^2-24x-16\)
\(=6x^3+24x^2+30x+9\)
Áp dụng HĐT \(a^3-b^3=\left(a-b\right)^3+3ab\left(a-b\right)\)
\(M=\left(-2\right)^3+3\left(x+y-1\right)\left(x+y+1\right)\left(-2\right)+6\left(x+y\right)^2\)
\(=-8-6\left[\left(x+y\right)^2-1\right]+6\left(x+y\right)^2\)
\(=-2\)
