\(\left(x^2+4x-5\right)\left(x^2+4x-21\right)=297\)
đặt a = \(x^2+4x-5\) vào bt ta được:
\(a\left(a-16\right)-297=0\Leftrightarrow a^2-16a+64-361=0\)
\(\Leftrightarrow\left(a-8\right)^2-19^2=0\Leftrightarrow\left(a-27\right)\left(a+11\right)=0\)
\(\Leftrightarrow\left(x^2+4x-32\right)\left(x^2+4+6\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x+8\right)\left(\left(x+2\right)^2+2\right)=0\)
\(\left\{{}\begin{matrix}x-4=0\\x+8=0\\\left(x+2\right)^2=-2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=4\\x=-8\end{matrix}\right.\)
\(\left(x-1\right)\left(x-3\right)\left(x+5\right)\left(x+7\right)=297\)
\(\Leftrightarrow\left(x^2-3x-x+3\right)\left(x^2+7x+5x+35\right)=297\)
\(\Leftrightarrow\left(x^2-4x+3\right)\left(x^2+12x+35\right)=297\)
\(\Leftrightarrow x^4+12x^3+35x^2-4x^3-48x^2-140x+3x^2+36x+105=297\)
\(\Leftrightarrow x^4+8x^3-10x^2-104x+105-297=0\)
\(\Leftrightarrow x^4-4x^3+12x^3-48x^2+38x^2-152x+48x-192=0\)
\(\Leftrightarrow x^3\left(x-4\right)+12x^2\left(x-4\right)+38x\left(x-4\right)+48\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x^3+12x^2+38x+48\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x^3+8x^2+4x^2+32x+6x+48\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left[x^2\left(x+8\right)+4x\left(x+8\right)+6\left(x+8\right)\right]=0\)
\(\Leftrightarrow\left(x-4\right)\left(x+8\right)\left(x^2+4x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x+8=0\\x^2+4x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-8\\x\notin R\end{matrix}\right.\)
\(S=\left\{4;-8\right\}\)
\(\left(x-1\right)\left(x+5\right)\left(x-3\right)\left(x+7\right)-297=0\)
\(\Leftrightarrow\left(x^2+4x-5\right)\left(x^2+4x-21\right)-297=0\)
gọi \(x^2+4x-5=y\) ta có :
\(y\left(y-16\right)-297=0\)
\(\Leftrightarrow y^2-16y-297=0\)
\(\Leftrightarrow\left(y-27\right)\left(y+11\right)=0\)
\(\Leftrightarrow\left(x^2-4x-32\right)\left(x^2-4x+6\right)=0\)
\(\Leftrightarrow\left(x-8\right)\left(x+4\right)\left(x^2-4x+6\right)=0\)
\(\Rightarrow\left(x-8\right)\left(x+4\right)=0\) ( VÌ \(x^2-4x+6=\left(x-2\right)^2+2\) )
còn lại tự làm :))
