giải phương trình: x^2010-2011x^670+căn bậc hai của 2010=0 13/09/2021 Bởi Eloise giải phương trình: x^2010-2011x^670+căn bậc hai của 2010=0
Đáp án: $\begin{array}{l} dat\,{x^{670}} = a(a \ge 0)\\ {x^{2010}} – 2011.{x^{670}} + \sqrt {2010} = 0\\ \Leftrightarrow {\left( a \right)^3} – 2010.a – a + \sqrt {2010} = 0\\ \Leftrightarrow a.\left[ {{{(a)}^2} – 2010} \right] – (a – \sqrt {2010} ) = 0\\ \Leftrightarrow a\left( {a – \sqrt {2010} } \right)\left( {a + \sqrt {2010} } \right) – (a – \sqrt {2010} ) = 0\\ \Leftrightarrow (a – \sqrt {2010} )\left[ {a.\left( {a + \sqrt {2010} } \right) – 1} \right] = 0\\ \Leftrightarrow \left[ {a = } \right.\sqrt {2010} \,hoac\,{a^2} + \sqrt {2010} a – 1 = 0\\ \Leftrightarrow {x^{670}} = \sqrt {2010} hoac\,{x^{670}} = 0,02229(do\,a \ge 0)\\ \Leftrightarrow x = \sqrt[{1340}]{{2010}}hoac\,x = 0,9943\\ \\ \end{array}$ Bình luận
datx670=a(a≥0)x2010−2011.x670+√2010=0⇔(a)3−2010.a−a+√2010=0⇔a.[(a)2−2010]−(a−√2010)=0⇔a(a−√2010)(a+√2010)−(a−√2010)=0⇔(a−√2010)[a.(a+√2010)−1]=0⇔[a=√2010hoaca2+√2010a−1=0⇔x670=√2010hoacx670=0,02229(doa≥0)⇔x=1340√2010hoacx=0,9943 Bình luận
Đáp án:
$\begin{array}{l}
dat\,{x^{670}} = a(a \ge 0)\\
{x^{2010}} – 2011.{x^{670}} + \sqrt {2010} = 0\\
\Leftrightarrow {\left( a \right)^3} – 2010.a – a + \sqrt {2010} = 0\\
\Leftrightarrow a.\left[ {{{(a)}^2} – 2010} \right] – (a – \sqrt {2010} ) = 0\\
\Leftrightarrow a\left( {a – \sqrt {2010} } \right)\left( {a + \sqrt {2010} } \right) – (a – \sqrt {2010} ) = 0\\
\Leftrightarrow (a – \sqrt {2010} )\left[ {a.\left( {a + \sqrt {2010} } \right) – 1} \right] = 0\\
\Leftrightarrow \left[ {a = } \right.\sqrt {2010} \,hoac\,{a^2} + \sqrt {2010} a – 1 = 0\\
\Leftrightarrow {x^{670}} = \sqrt {2010} hoac\,{x^{670}} = 0,02229(do\,a \ge 0)\\
\Leftrightarrow x = \sqrt[{1340}]{{2010}}hoac\,x = 0,9943\\
\\
\end{array}$
datx670=a(a≥0)x2010−2011.x670+√2010=0⇔(a)3−2010.a−a+√2010=0⇔a.[(a)2−2010]−(a−√2010)=0⇔a(a−√2010)(a+√2010)−(a−√2010)=0⇔(a−√2010)[a.(a+√2010)−1]=0⇔[a=√2010hoaca2+√2010a−1=0⇔x670=√2010hoacx670=0,02229(doa≥0)⇔x=1340√2010hoacx=0,9943