c)
\(\left(x^2-x+1\right)\left(x^2+x+1\right)\left(x-1\right)\left(x+1\right)=63\\ \Leftrightarrow\left[\left(x^2+1\right)^2-x^2\right]\left(x^2-1\right)=63\\ \Leftrightarrow\left(x^2+1\right)^2\left(x^2-1\right)-x^2\left(x^2-1\right)=63\\ \Leftrightarrow\left(x^2+1\right)\left(x^4-1\right)-x^4+x^2=63\\ \Leftrightarrow x^6-x^2+x^4-1-x^4+x^2=63\\ \Leftrightarrow x^6-1=63\\ \Leftrightarrow x^6=64\\ \Leftrightarrow x^6=\left(\pm2\right)^6\\ \Leftrightarrow x=\pm2\)
b)
\(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)=\left(x^2+8x+11\right)^2+2x\\ \Leftrightarrow\left[\left(x+1\right)\left(x+7\right)\right]\left[\left(x+3\right)\left(x+5\right)\right]=\left(x^2+8x+11\right)^2+2x\\ \Leftrightarrow\left(x^2+8x+7\right)\left(x^2+8x+15\right)=\left(x^2+8x+11\right)^2+2x\\ \Leftrightarrow\left[\left(x^2+8x+11\right)-4\right]\left[\left(x^2+8x+11\right)+4\right]=\left(x^2+8x+11\right)^2+2x\\ \Leftrightarrow\left(x^2+8x+11\right)^2-16=\left(x^2+8x+11\right)^2+2x\\ \Leftrightarrow2x=-16\\ \Leftrightarrow x=-8\)
(câu a làm tương tự nhé)
