Hãy luôn nhớ cảm ơn và vote 5*
nếu câu trả lời hữu ích nhé!
5725
3937
$\begin{array}{l}
\sqrt {{x^2} - x + 1} = \dfrac{{{x^3} + 3{x^2} - 4x + 1}}{{{x^2} + 3}}\\
D = \mathbb R\\
\Leftrightarrow \sqrt {{x^2} - x + 1} = \dfrac{{x\left( {{x^2} + 3} \right) + 3\left( {{x^2} + 3} \right) - 7x - 8}}{{{x^2} + 3}}\\
\Leftrightarrow \sqrt {{x^2} - x + 1} = x + 3 - \dfrac{{7x + 8}}{{{x^2} + 3}}\\
\Leftrightarrow \sqrt {{x^2} - x + 1} - \left( {x + 3} \right) + \dfrac{{7x + 8}}{{{x^2} + 3}} = 0\\
\Leftrightarrow \dfrac{{{x^2} - x + 1 - {x^2} - 6x + 9}}{{\sqrt {{x^2} - x + 1} + \left( {x + 3} \right)}} + \dfrac{{7x + 8}}{{{x^2} + 3}} = 0\\
\Leftrightarrow \dfrac{{ - 7x - 8}}{{\sqrt {{x^2} - x + 1} + \left( {x + 3} \right)}} + \dfrac{{7x + 8}}{{{x^2} + 3}} = 0\\
\Leftrightarrow \left( {7x + 8} \right)\left( {\dfrac{1}{{{x^2} + 3}} - \dfrac{1}{{\sqrt {{x^2} - x + 1} + \left( {x + 3} \right)}}} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = - \dfrac{8}{7}\\
\dfrac{1}{{\sqrt {{x^2} - x + 1} + \left( {x + 3} \right)}} = \dfrac{1}{{{x^2} + 3}}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - \dfrac{8}{7}\\
\sqrt {{x^2} - x + 1} = {x^2} - x\left( * \right)
\end{array} \right.\\
\left( * \right):t = \sqrt {{x^2} - x + 1} \Rightarrow {x^2} - x + 1 = {t^2} \Rightarrow {x^2} - x = {t^2} - 1\\
\left( * \right) \Leftrightarrow t = {t^2} - 1\\
\Leftrightarrow {t^2} - t - 1 = 0 \Leftrightarrow t = \dfrac{{1 + \sqrt 5 }}{2},t = \dfrac{{1 - \sqrt 5 }}{2}\\
\Rightarrow \left[ \begin{array}{l}
\sqrt {{x^2} - x + 1} = \dfrac{{1 + \sqrt 5 }}{2}\\
\sqrt {{x^2} - x + 1} = \dfrac{{1 - \sqrt 5 }}{2}
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
{x^2} - x + 1 = \dfrac{{3 + \sqrt 5 }}{2}\\
{x^2} - x + 1 = \dfrac{{3 - \sqrt 5 }}{2}
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
{x^2} - x - \dfrac{{1 + \sqrt 5 }}{2} = 0\\
{x^2} - x + \dfrac{{\sqrt 5 - 1}}{2} = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{1 + \sqrt {3 + 2\sqrt 5 } }}{2}\\
x = \dfrac{{1 - \sqrt {3 - 2\sqrt 5 } }}{2}
\end{array} \right.\\
\Rightarrow S = \left\{ {\dfrac{{1 + \sqrt {3 + 2\sqrt 5 } }}{2};\dfrac{{1 - \sqrt {3 - 2\sqrt 5 } }}{2}; - \dfrac{8}{7}} \right\}
\end{array}$
Hãy giúp mọi người biết câu trả lời này thế nào?
Bảng tin
0
130
0
Cảm ơn bạn rất nhiều