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Tìm x, biết:
a) \(x(x – 5) + x – 5 = 0\) ;
b) \(7x(x – 4) – x + 4 = 0\) ;
c) \(({x^2} – 4x) – 5x + 20 = 0\) ;
d) \({x^3} – 3{x^2} + x – 3 = 0\) .
Phối hợp các phương pháp.
\(\eqalign{ & a)\,\,x\left( {x – 5} \right) + x – 5 = 0 \cr & \,\,\,x\left( {x – 5} \right) + \left( {x – 5} \right) = 0 \cr & \,\,\,\,\,\,\,\,\,\,\,\left( {x – 5} \right)\left( {x + 1} \right) = 0 \cr} \)
\(x – 5 = 0\) hoặc \(x + 1 = 0\)
\(x = 5\) hoặc \(x = – 1\)
\(\eqalign{ & b)\,\,7x\left( {x – 4} \right) – x + 4 = 0 \cr & \,\,7x\left( {x – 4} \right) – \left( {x – 4} \right) = 0 \cr & \,\,\,\,\,\,\,\,\,\,\,\left( {x – 4} \right)\left( {7x – 1} \right) = 0 \cr} \)
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\(x – 4 = 0\) hoặc \(7x – 1 = 0\)
\(x – 4 = 0\) hoặc \(7x = 1\)
\(x = 4\) hoặc \(x = {1 \over 7}\)
\(\eqalign{ & c)\,\,\left( {{x^2} – 4x} \right) – 5x + 20 = 0 \cr & \,\,\,\,\,\,x\left( {x – 4} \right) – 5\left( {x – 4} \right) = 0 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {x – 4} \right)\left( {x – 5} \right) = 0 \cr} \)
\(x – 4 = 0\) hoặc \(x – 5 = 0\)
\(x = 4\) hoặc \(x = 5\)
\(\eqalign{ & d)\,\,{x^3} – 3{x^2} + x – 3 = 0 \cr & \,{x^2}\left( {x – 3} \right) + \left( {x – 3} \right) = 0 \cr & \,\,\,\,\,\,\,\,\left( {x – 3} \right)\left( {{x^2} + 1} \right) = 0 \cr} \)
\(x – 3 = 0\) (vì \({x^2} + 1 > 0\) với mọi x).
\(x = 3\)