Câu 4 nhé mn!!!!!!!!!!!!!!!!! Question Câu 4 nhé mn!!!!!!!!!!!!!!!!! in progress 0 Môn Toán Mít Mít 4 years 2020-10-20T04:34:39+00:00 2020-10-20T04:34:39+00:00 1 Answers 68 views 0
Answers ( )
Đáp án:
$\begin{array}{l}
a)x = \dfrac{3}{2}\\
b)x = \dfrac{{ – 1}}{2}\\
c)x = 7\\
d)x = 14
\end{array}$
Giải thích các bước giải:
$\begin{array}{l}
a)\left( {x – 1} \right)\left( {{x^2} + x + 1} \right) – x\left( {x + 2} \right)\left( {x – 2} \right) = 5\\
\Leftrightarrow {x^3} – 1 – x\left( {{x^2} – 4} \right) – 5 = 0\\
\Leftrightarrow {x^3} – 1 – {x^3} + 4x – 5 = 0\\
\Leftrightarrow 4x – 6 = 0\\
\Leftrightarrow x = \dfrac{3}{2}\\
b){\left( {x + 1} \right)^3} – {\left( {x – 1} \right)^3} – 6{\left( {x – 1} \right)^2} = – 10\\
\Leftrightarrow \left( {x + 1 – \left( {x – 1} \right)} \right)\left[ {{{\left( {x + 1} \right)}^2} + \left( {x + 1} \right)\left( {x – 1} \right) + {{\left( {x – 1} \right)}^2}} \right] – 6{\left( {x – 1} \right)^2} + 10 = 0\\
\Leftrightarrow 2\left[ {{x^2} + 2x + 1 + {x^2} – 1 + {x^2} – 2x + 1} \right] – 6\left( {{x^2} – 2x + 1} \right) + 10 = 0\\
\Leftrightarrow 2\left( {3{x^2} + 1} \right) – 6{x^2} + 12x – 6 + 10 = 0\\
\Leftrightarrow 6{x^2} + 2 – 6{x^2} + 12x + 4 = 0\\
\Leftrightarrow 12x + 6 = 0\\
\Leftrightarrow x = \dfrac{{ – 1}}{2}\\
c)\left( {x – 3} \right)\left( {{x^2} + 3x + 9} \right) + x\left( {x + 2} \right)\left( {2 – x} \right) = 1\\
\Leftrightarrow {x^3} – 27 – x\left( {x + 2} \right)\left( {x – 2} \right) – 1 = 0\\
\Leftrightarrow {x^3} – 27 – x\left( {{x^2} – 4} \right) – 1 = 0\\
\Leftrightarrow {x^3} – 27 – {x^3} + 4x – 1 = 0\\
\Leftrightarrow 4x – 28 = 0\\
\Leftrightarrow x = 7\\
d){\left( {x – 1} \right)^3} – \left( {x + 3} \right)\left( {{x^2} – 3x + 9} \right) + 3\left( {{x^2} – 4} \right) = 2\\
\Leftrightarrow {\left( {x – 1} \right)^3} – \left( {{x^3} + 27} \right) + 3{x^2} – 12 – 2 = 0\\
\Leftrightarrow {x^3} – 3{x^2} + 3x – 1 – {x^3} – 27 + 3{x^2} – 14 = 0\\
\Leftrightarrow 3x – 42 = 0\\
\Leftrightarrow x = 14
\end{array}$