Toán Lớp 9: (x+1)(x+2)(x+3)^2(x+4)(x+5)=360
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Toán Lớp 9: (x+1)(x+2)(x+3)^2(x+4)(x+5)=360
Comments ( 1 )
\left( {x + 1} \right)\left( {x + 2} \right){\left( {x + 3} \right)^2}\left( {x + 4} \right)\left( {x + 5} \right) = 360\\
\Leftrightarrow \left( {x + 1} \right)\left( {x + 5} \right)\left( {x + 2} \right)\left( {x + 4} \right){\left( {x + 3} \right)^2} = 360\\
\Leftrightarrow \left( {{x^2} + 6x + 5} \right)\left( {{x^2} + 6x + 8} \right)\left( {{x^2} + 6x + 9} \right) = 360\\
Dat:{x^2} + 6x + 5 = a\\
\Leftrightarrow a.\left( {a + 3} \right)\left( {a + 4} \right) = 360\\
\Leftrightarrow {a^3} + 7{a^2} + 12a – 360 = 0\\
\Leftrightarrow {a^3} – 5{a^2} + 12{a^2} – 60a + 72a – 360 = 0\\
\Leftrightarrow \left( {a – 5} \right)\left( {{a^2} + 12a + 72} \right) = 0\\
\Leftrightarrow a – 5 = 0\\
\Leftrightarrow {x^2} + 6x + 5 – 5 = 0\\
\Leftrightarrow x\left( {x + 6} \right) = 0\\
\Leftrightarrow x = 0/x = – 6\\
Vậy\,x = 0;x = – 6
\end{array}$