198.
a/ x³ - 3x² + 4 = 0
⇔ x³ - x² - 4x² + 4 = 0
⇔ x² ( x + 1 ) - 4 ( x - 1 ) ( x + 1 ) = 0
⇔ ( x + 1 ) ( x² - 4x + 4 ) = 0
⇔ ( x + 1 ) ( x - 2 )² = 0
⇔ \(\left[ \begin{array}{l}x+1=0\\x-2=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=-1\\x=2\end{array} \right.\)
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b/ $x^{4}$ + $x^{3}$ - $4x^{2}$ + $5x$ - $3$ = $0$
⇔ ( x - 1 ) ( x³ + 2x² - 2x + 3 ) = 0
⇔ ( x - 1 ) [( x³ + 3 + 3x² ) - ( x² + 3x ) + ( 3x + 3 )] = 0
⇔ ( x - 1 ) ( x + 3 ) ( x² - 3x + 3 ) = 0
⇔ \(\left[ \begin{array}{l}x-1=0\\x+3=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=1\\x=-3\end{array} \right.\)
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199.
$4^{x}$ - $10.2^{x}$ + $16$ = $0$
⇔ ( $2^{x}$ - 5 )² - 9 = 0
⇔ ( $2^{x}$ - 5 - 3 ) ( $2^{x}$ - 5 + 3 ) = 0
⇔ ( $2^{x}$ - 8 ) ( $2^{x}$ - 2 ) = 0
⇔ \(\left[ \begin{array}{l}2^x-8=0\\2^x-2=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=3\\x=1\end{array} \right.\)
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