GIẢI PHƯƠNG TRÌNH SAU:

A, X mũ 4 + 2x mũ 3 - 4x bình - 5x - 6=0

B, X mũ 4 - 2x mũ 3 + x -2=0

C, X mũ 4 +2x mũ 3 + 5x bình -4x -12=0

_ GIÚP MÌNH VỚI Ạ !!!!

Đáp án + Giải thích các bước giải

` a) x^4 + 2x^3 - 4x^2 - 5x - 6 = 0 `

` => x^4 + 4x^3 - 2x^3 + 4x^2 + - 8x^2 + 3x- 8x - 6=  0 `

` => (x^4 + 4x^3 + 4x^2 + 3x ) - ( 2x^3 + 8x^2 + 8x + 6 ) = 0 `

` => x(x^3 + 4x^2 + 4x + 3 ) - 2( x^3 + 4x + 4x^2 + 3 ) = 0 `

` => (x-2)(x^3 + 4x^2 + 4x + 3 ) = 0 `

` => (x-2)(x+3)(x^2+x+1)=0 `

` x^2+x+1 > 0 ∀ x ` 

` ⇒ x^2+x+1=0 ` $\text{(Loại)}$

` => ` \(\left[ \begin{array}{l}x-2=0\\x+3=0\end{array} \right.\) 

` => ` \(\left[ \begin{array}{l}x=2\\x=-3\end{array} \right.\) 

` b) x^4 - 2x^3 + x - 2 = 0 `

` => ( x^4 + x ) - ( 2x^3 + 2 ) = 0 `

` => x(x^3 + 1 ) - 2(x^3+1)=0 `

` => (x-2)(x^3+1)=0 `

` ⇒ ` \(\left[ \begin{array}{l}x-2=0\\x^3+1=0\end{array} \right.\) 

` => ` \(\left[ \begin{array}{l}x=2\\x=-1\end{array} \right.\) 

` c) x^4 + 2x^3 + 5x^2 - 4x - 12 = 0 ` 

` => x^4 - x^3 + 3x^3 - 3x^2 + 8x^2 - 8x + 12x - 12 = 0 `

` => ( x^4 - x^3 ) + ( 3x^3 - 3x^2 ) + ( 8x^2 - 8x ) + ( 12x - 12 ) = 0 `

` => x^3 ( x - 1 ) + 3x^2 ( x - 1 ) + 8x ( x - 1 ) + 12( x - 1 ) = 0 `

` => ( x - 1 ) ( x^3 + 3x^2 + 8x + 12 ) = 0 `

` ⇒ ( x - 1 ) ( x^3 + x^2 + 2x^2 + 2x + 6x + 12 ) = 0 `

` => ( x - 1 ) [ ( x^3 + x^2 + 6x ) + ( 2x^2 + 2x + 12 ) ] = 0 `

` => ( x-1 ) [ x(x^2 + x + 6) + 2(x^2 + 1 + 6)] = 0 `

` => (x-1) (x+2) ( x^2 + x + 6 ) = 0 `

` x^2 + x + 6 > 0 ∀ x `

` => x^2 + x + 6 = 0 ` $\text{(Loại)}$ 

` ⇒ ` \(\left[ \begin{array}{l}x-1=0\\x+2=0\end{array} \right.\) 

` => ` \(\left[ \begin{array}{l}x=1\\x=-2\end{array} \right.\)