Toán Lớp 8: Xác định a,b để x^2+bx-a=2x(x-1)-x(x+b) +1
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Toán Lớp 8: Xác định a,b để x^2+bx-a=2x(x-1)-x(x+b) +1
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{x^2} + bx – a = 2x\left( {x – 1} \right) – x\left( {x + b} \right) + 1\\
\Leftrightarrow {x^2} + bx – a = \left( {2{x^2} – 2x} \right) – \left( {{x^2} + bx} \right) + 1\\
\Leftrightarrow {x^2} + bx – a = 2{x^2} – 2x – {x^2} – bx + 1\\
\Leftrightarrow {x^2} + bx – a = {x^2} – 2x – bx + 1\\
\Leftrightarrow {x^2} + bx – a – {x^2} + 2x + bx – 1 = 0\\
\Leftrightarrow \left( {{x^2} – {x^2}} \right) + \left( {bx + 2x + bx} \right) + \left( { – a – 1} \right) = 0\\
\Leftrightarrow x.\left( {b + 2 + b} \right) – \left( {a + 1} \right) = 0\\
\Leftrightarrow x.\left( {2b + 2} \right) – \left( {a + 1} \right) = 0\\
\Rightarrow \left\{ \begin{array}{l}
2b + 2 = 0\\
a + 1 = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
b = – 1\\
a = – 1
\end{array} \right. \Rightarrow a = b = – 1
\end{array}\)