$ a )x^{4}-$ $2x^{3}+$ $10x^{2}-20x=0$
$\text{ <=> }$ $x^{3}( x-2)+10x(x-2)=0$
$\text{ <=> x ( }$ $x^{}-2)($$x^{2}+10)=0$
$\text{ <=> x ( x - 2 ) (}$ $x^{2}+10)=0$
$<=>\left[\begin{array}{ccc}x=0\\x-2=0\\x^{2}+10=0 (ktm)\end{array}\right]<=>$ \(\left[ \begin{array}{l}x=0\\x=2\end{array} \right.\)
$\text{ x ∈ (0 ; }$ $2 ^{} )$
$\text{b ) ( 2x - 3 )}$$^{2}=(x+5)$$^{2}$
$\text{ <=>}$ $(2x - 3 )^{2}-(x+5)$$^{2}=0$
$\text{ <=> ( 2x - 3 + x + 5 ) ( 2x - 3 - x - 5 ) = 0}$
$\text{ <=> ( 3x + 2 ) ( x - 8 ) = 0}$
<=>\(\left[ \begin{array}{l} 3x + 2 =0\\ x - 8 =0\end{array} \right.\) <=>\(\left[ \begin{array}{l}x=- \dfrac{2}{3}\\x=8\end{array} \right.\)
$\text{ x ∈ (} $ $-\dfrac{2}{3};8 )$
$c ) x^{2}(x-1)-$ $4x^{2}+8x-4=0$
$<=> x^{2}(x-1)-($ $4x^{2}-8x+4)=0$
$<=> x^{2}(x-1)-($ $4x^{2}-4x-4x+4)=0$
$<=> x^{2}(x-1)-$$\text{ [ 4x ( x - 1) - 4 ( x - 1) ]=0}$
$<=> x^{2}(x-1)- (4x-4)(x-1)=0$
$<=>(x^{2}-4x+4)(x-1)=0$
$<=>(x^{2}-4x+4)(x-1)=0$
$<=>(x-2)^{2}(x-1)=0$
<=>\(\left[ \begin{array}{l}x-2=0\\x-1=0\end{array} \right.\) <=>\(\left[ \begin{array}{l}x=2\\x=1\end{array} \right.\)
$\text{ x ∈ (1 ; }$ $2 ^{})$
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