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Ta có :
\(\left\{{}\begin{matrix}7x-3y=5\\\frac{x}{2}+\frac{y}{3}=2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}7x-3y=5\\\frac{3x+2y}{6}=2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}7x-3y=5\\3x+2y=12\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}14x-6y=10\\9x+6y=36\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}23x=46\\7x-3y=5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)
Vậy...
\(\left\{{}\begin{matrix}7x-3y=5\\\frac{x}{2}+\frac{y}{3}=2\end{matrix}\right.\) \(\left\{{}\begin{matrix}7x-3y=5\\3x+2y=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}14x-6y=10\\9x+6y=36\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}23x=46\\7x-3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)
Vậy hpt có 1 nghiệm duy nhất (x;y) =(2;3)
<=> \(\hept{\begin{cases}7x-3y=5\\3x+2y=12\end{cases}}\) <=> \(\hept{\begin{cases}21x-9y=15\\21x+14y=84\end{cases}}\) <=> \(\hept{\begin{cases}-23y=-69\\3x+2y=12\end{cases}}\) <=> \(\hept{\begin{cases}y=3\\x=\frac{12-2y}{3}=\frac{12-2.3}{3}=2\end{cases}}\)
Vậy nghiệm của hpt là: (2;3)
\(\left\{{}\begin{matrix}7x-3y=5\\\frac{x}{2}+\frac{y}{3}=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{3y+5}{7}\\\frac{3y+5}{14}+\frac{y}{3}=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)
Vậy...
\(\hept{\begin{cases}7x-3y=4\\4x+y=5\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}7x-3y=4\\12x+3y=15\end{cases}}\)
Cộng vế ta được :
\(7x-3y+12x+3y=4+15\)
\(\Leftrightarrow19x=19\)
\(\Leftrightarrow x=1\)
Khi đó : \(7-3y=4\Leftrightarrow y=1\)
Vậy \(x=y=1\)
a) \(x^4-9x^2+20=0\)
\(\Leftrightarrow x^4-4x^2-5x^2+20=0\)
\(\Leftrightarrow x^2\left(x^2-4\right)-5\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x^2-4\right)\left(x^2-5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2-4=0\\x^2-5=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x\in\left\{\pm2\right\}\\x\in\left\{\pm\sqrt{5}\right\}\end{cases}}\)
Vậy....
\(x^4-9x^2+20=0\)
\(\Leftrightarrow x^4-4x^2-5x^2+20=0\)
\(\Leftrightarrow x^2\left(x^2-4\right)-5\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x^2-5\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2-5=0\\x^2-4=0\end{cases}}\Leftrightarrow x\in\left\{\pm2\right\}\)