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Câu 22 trang 205 SGK Đại số và Giải tích 11 Nâng cao

Tìm các nghiệm của phương trình sau
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Tìm các nghiệm của phương trình sau (làm tròn kết quả nghiệm gần đúng đến hàng phần nghìn)

LG a

\(f'\left( x \right) = 0\) \(\text{ với }\,f\left( x \right) = {{{x^3}} \over 3} - 2{x^2} - 6x - 1\)

Phương pháp giải:

Tính f'(x) và giải các phương trình.

Lời giải chi tiết:

\(\eqalign{  & f'\left( x \right) = {x^2} - 4x - 6  \cr  & f'\left( x \right) = 0 \Leftrightarrow {x^2} - 4x - 6 = 0  \cr  &  \Leftrightarrow \left[ {\matrix{   {x = 2 - \sqrt {10}  \approx  - 1,162}  \cr   {x = 2 + \sqrt {10}  \approx 5,162}  \cr  } } \right. \cr} \)

LG b

 \(f'\left( x \right) =  - 5\) \(\text{ với }\,f\left( x \right) = {{{x^4}} \over 4} - {x^3} - {{3{x^2}} \over 2} - 3.\)

Lời giải chi tiết:

Ta có: \(f'(x) = {x^3} - 3{x^2} - 3x.\) Do đó : \(\eqalign{  & f'(x)+ 5 = 0 \cr &\Leftrightarrow {x^3} - 3{x^2} - 3x + 5 = 0  \cr  &  \Leftrightarrow \left( {x - 1} \right)\left( {{x^2} - 2x - 5} \right) = 0 \cr} \)

\( \Leftrightarrow \left[ \begin{array}{l}
x - 1 = 0\\
{x^2} - 2x - 5 = 0
\end{array} \right.\) \( \Leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = 1 \pm \sqrt 6
\end{array} \right.\)

Phương trình có ba nghiệm là \(1;1 + \sqrt 6 \;\text{ và }\,1 - \sqrt 6 \) Vậy các nghiệm gần đúng của phương trình là : \(\eqalign{  & {x_1} = 1  \cr  & {x_2}  \approx  3,449   \cr  & {x_3}  \approx   - 1,449  \cr} \)

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