Toán Lớp 8: Tìm x’
e. ( 3x – 1)2 – ( x +5)2=0
f. ( 2x -1)2 – ( x -3)2=0
g.(2x -1)2- (4×2 – 1) = 0
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Toán Lớp 8: Tìm x’
e. ( 3x – 1)2 – ( x +5)2=0
f. ( 2x -1)2 – ( x -3)2=0
g.(2x -1)2- (4×2 – 1) = 0
Comments ( 2 )
e.{\rm{ }}{\left( {{\rm{ }}3x{\rm{ }}–{\rm{ }}1} \right)^2}{\rm{ }}–{\rm{ }}{\left( {{\rm{ }}x{\rm{ }} + 5} \right)^2} = 0\\
\Leftrightarrow {(3x)^2} + 2.3x + 1 – 4({x^2} – 2.x.3 + {3^2}) = 0\\
\Leftrightarrow 9{x^2} + 6x + 1 – 4{x^2} + 24x – 36 = 0\\
\Leftrightarrow 5{x^2} + 30x – 35 = 0\\
\Leftrightarrow 5({x^2} + 2.x.3 + {3^2}) – 80 = 0\\
\Leftrightarrow 5{(x + 3)^2} = 80\\
\Leftrightarrow {(x + 3)^2} = 16\\
\Rightarrow \left[ \begin{array}{l}
x + 3 = 4\\
x + 3 = – 4
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 1\\
x = – 7
\end{array} \right.\\
f.{\rm{ }}{\left( {{\rm{ }}2x{\rm{ }} – 1} \right)^2}{\rm{ }}–{\rm{ }}{\left( {{\rm{ }}x{\rm{ }} – 3} \right)^2} = 0\\
\Leftrightarrow 4x – 2 – 2x – 6 = 0\\
\Leftrightarrow 2x – 8 = 0\\
\Leftrightarrow 2x = 0 + 8\\
\Leftrightarrow 2x = 8\\
\Leftrightarrow x = 8:2\\
\Leftrightarrow x = 4\\
g.{\left( {2x{\rm{ }} – 1} \right)^2} – {\rm{ }}\left( {4{x^2}{\rm{ }}–{\rm{ }}1} \right){\rm{ }} = {\rm{ }}0\\
\Leftrightarrow {(2x)^2} – 2.2x.1 + {1^2} – 4{x^2} + 1 = 0\\
\Leftrightarrow 4{x^2} – 4x + 1 – 4{x^2} + 1 = 0\\
\Leftrightarrow 2 – 4x = 0\\
\Leftrightarrow – 4x = – 2\\
\Leftrightarrow 4x = 2\\
\Leftrightarrow x = 2:4\\
\Leftrightarrow x = \frac{1}{2}
\end{array}\]