Toán Lớp 8: Tìm GtNN của 2x+5x^2
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Toán Lớp 8: Tìm GtNN của 2x+5x^2
Mn help me
Comments ( 1 )
2x + 5{x^2}\\
= 5{x^2} + 2.x\sqrt 5 .\dfrac{1}{{\sqrt 5 }} + \dfrac{1}{5} – \dfrac{1}{5}\\
= {\left( {x\sqrt 5 + \dfrac{1}{{\sqrt 5 }}} \right)^2} – \dfrac{1}{5}\\
Do:{\left( {x\sqrt 5 + \dfrac{1}{{\sqrt 5 }}} \right)^2} \ge 0\forall x\\
\to {\left( {x\sqrt 5 + \dfrac{1}{{\sqrt 5 }}} \right)^2} – \dfrac{1}{5} \ge – \dfrac{1}{5}\\
\to Min = – \dfrac{1}{5}\\
\Leftrightarrow x\sqrt 5 + \dfrac{1}{{\sqrt 5 }} = 0\\
\to x = – \dfrac{1}{5}
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