Trả lời giúp mik mấy câu này đi! Dễ lắm!! 1) ( $2x^{2}$ +x +1) ($2x^{2}$ +x+4)= -4 2) $4x^{3}$ -$4x^{2}$ -15x+18 =0 3) $x^{4}$ +$2x^{3}$ -$4x^{2}$ -5x

Question

Trả lời giúp mik mấy câu này đi! Dễ lắm!!
1) ( $2x^{2}$ +x +1) ($2x^{2}$ +x+4)= -4
2) $4x^{3}$ -$4x^{2}$ -15x+18 =0
3) $x^{4}$ +$2x^{3}$ -$4x^{2}$ -5x-6=0
4) $x^{4}$ -$5x^{3}$ +$7x^{2}$ -5x+1=0
5) $(x+2)^{4}$ +$(x+4)^{4}$ =16
Làm ơn!!!! Hứa tặng 5*!!!

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Sarah 3 tháng 2021-08-31T02:40:27+00:00 1 Answers 6 views 0

Answers ( )

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    2021-08-31T02:41:28+00:00

    `1)(2x^2+x+1)(2x^2+x+4)=-4`

    `<=>4x^4+4x^3+11x^2+5x+4=-4`

    `<=>4x^4+4x^3+11x^2+5x+4+4=-4+4`

    `<=>4x^4+4x^3+11x^2+5x+4+4=0`

    Vậy `x∈ZZ`

     `2)4x^3-4x^2-15x+18=0`

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

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

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

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

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

    `<=>(x^2+x+1)(x^2-2x+3x-6)=0`

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

    Ta có : `x^2+x+1>0∀x` nên vô nghiệm

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

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

    `4)x^4-5x^3+7x^2-5x+1=0`

    `<=>x^3-4.69847…x^2+5.58330…x-3.31651… ≈0`

    `<=>x^2-1.38196…x+1.00000… ≈0`

    `<=>x ≈0.30152… +1.00000≈0`

    `5)(x+2)^4+(x+4)^4=16`

    `<=>2x^4+24x^3+120x^2+288x+272=16`

    `<=>2x^4+24x^3+120x^2+288x+272-16=16-16`

    `<=>2x^4+24x^3+120x^2+288x+256=0`

    `<=>2(x+2)(x+4)(x^2+6x+16)=0`

    `<=>` \(\left[ \begin{array}{l}x+2=0\\x+4=0\\x^2+6x+16=0\end{array} \right.\)

    `<=>` \(\left[ \begin{array}{l}x=-2\\x=-4\\x=-3+\sqrt[]{7};-3-\sqrt[]{7}\end{array} \right.\)

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