Đáp án:
a)x = { -3; -2}
b)$x^{4}$ + 5x³ + 9x² + 5x + 1=0
c)Vậy x ={1;2}
Giải thích các bước giải:
a) ( x + 3)² - ( x + 3) = 0
⇔( x + 3) ( x + 3) - ( x + 3) = 0
⇔ ( x + 3) ( x + 3 - 1) = 0
⇔ ( x + 3) ( x + 2) = 0
⇔\(\left[ \begin{array}{l}x + 3 = 0\\x + 2 = 0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-3\\x=-2\end{array} \right.\)
Vậy x = { -3; -2}
b) ( x + 1)² - x³ . $( x + 1)^{4}$ = 0
⇔ $(x + 1)^{6}$ - x³ = 0
⇔[ ( x + 1)²]³ - x³ = 0
⇔ [ ( x + 1) - x] [ ( x + 1)²]² + x. ( x + 1)² + x²] =0
⇔$x^{4}$ + 4x³ + 6x² + 4x + 1 + x³ + 2x² + x + x²=0
⇔ $x^{4}$ + 5x³ + 9x² + 5x + 1=0
Vậy $x^{4}$ + 5x³ + 9x² + 5x + 1=0
c) ( 1 - x)² + ( 1 - x) = 0
⇔ ( 1 - x) ( 1 - x + 1) = 0
⇔ ( 1 - x) ( 2 - x) = 0
⇔\(\left[ \begin{array}{l}1 - x = 0\\2 - x = 0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x = 1\\x=2\end{array} \right.\)
Vậy x ={1;2}
