Toán Lớp 8: a) (x -5)(x -4) – (x + 1)(x -2) = 7
b) 5x(x-3)=(x-2)(5x-1)-5
c) (x-5)(x-1)=(x-1)(x-2)
d)6(x-3)(x-4)-6x(x-2)=4
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Toán Lớp 8: a) (x -5)(x -4) – (x + 1)(x -2) = 7
b) 5x(x-3)=(x-2)(5x-1)-5
c) (x-5)(x-1)=(x-1)(x-2)
d)6(x-3)(x-4)-6x(x-2)=4
Comments ( 1 )
a,\\
x = \dfrac{{15}}{8}\\
b,\\
x = \dfrac{3}{4}\\
c,\\
x = 1\\
d,\\
x = \dfrac{{34}}{{15}}
\end{array}\)
a,\\
\left( {x – 5} \right)\left( {x – 4} \right) – \left( {x + 1} \right)\left( {x – 2} \right) = 7\\
\Leftrightarrow \left( {{x^2} – 4x – 5x + 20} \right) – \left( {{x^2} – 2x + x – 2} \right) = 7\\
\Leftrightarrow \left( {{x^2} – 9x + 20} \right) – \left( {{x^2} – x – 2} \right) = 7\\
\Leftrightarrow {x^2} – 9x + 20 – {x^2} + x + 2 – 7 = 0\\
\Leftrightarrow – 8x + 15 = 0\\
\Leftrightarrow 8x = 15\\
\Leftrightarrow x = \dfrac{{15}}{8}\\
b,\\
5x\left( {x – 3} \right) = \left( {x – 2} \right)\left( {5x – 1} \right) – 5\\
\Leftrightarrow 5{x^2} – 15x = \left( {5{x^2} – x – 10x + 2} \right) – 5\\
\Leftrightarrow 5{x^2} – 15x = 5{x^2} – 11x – 3\\
\Leftrightarrow 5{x^2} – 15x – 5{x^2} + 11x + 3 = 0\\
\Leftrightarrow – 4x + 3 = 0\\
\Leftrightarrow 4x = 3\\
\Leftrightarrow x = \dfrac{3}{4}\\
c,\\
\left( {x – 5} \right)\left( {x – 1} \right) = \left( {x – 1} \right)\left( {x – 2} \right)\\
\Leftrightarrow \left( {x – 5} \right)\left( {x – 1} \right) – \left( {x – 1} \right)\left( {x – 2} \right) = 0\\
\Leftrightarrow \left( {x – 1} \right).\left[ {\left( {x – 5} \right) – \left( {x – 2} \right)} \right] = 0\\
\Leftrightarrow \left( {x – 1} \right).\left( {x – 5 – x + 2} \right) = 0\\
\Leftrightarrow \left( {x – 1} \right).\left( { – 3} \right) = 0\\
\Leftrightarrow x – 1 = 0\\
\Leftrightarrow x = 1\\
d,\\
6\left( {x – 3} \right)\left( {x – 4} \right) – 6x\left( {x – 2} \right) = 4\\
\Leftrightarrow 6.\left( {{x^2} – 4x – 3x + 12} \right) – \left( {6{x^2} – 12x} \right) = 4\\
\Leftrightarrow 6\left( {{x^2} – 7x + 12} \right) – \left( {6{x^2} – 12x} \right) = 4\\
\Leftrightarrow 6{x^2} – 42x + 72 – 6{x^2} + 12x – 4 = 0\\
\Leftrightarrow – 30x + 68 = 0\\
\Leftrightarrow 30x – 68 = 0\\
\Leftrightarrow 30x = 68\\
\Leftrightarrow x = \dfrac{{34}}{{15}}
\end{array}\)