giải bất phương trình : 1) x ³ – 6x ² – 7x – 5 < (x-2) ³ 2) x ²< (x+2) ² 3) 3 - 4x-1/18>x-1/12-4-5x/9 4)(2x-3)(x+3) ≥0 5)3x-1/4 – 3(x-2)/8-1>5-3x/2

0 bình luận về “giải bất phương trình : 1) x ³ – 6x ² – 7x – 5 < (x-2) ³ 2) x ²< (x+2) ² 3) 3 - 4x-1/18>x-1/12-4-5x/9 4)(2x-3)(x+3) ≥0 5)3x-1/4 – 3(x-2)/8-1>5-3x/2”

1. Đáp án:

    5) \(x > \dfrac{8}{5}\)

   Giải thích các bước giải:

   \(\begin{array}{l}
   1){x^3} – 6{x^2} – 7x – 5 < {\left( {x – 2} \right)^3}\\
    \to {x^3} – 6{x^2} – 7x – 5 < {x^3} – 6{x^2} + 12x – 8\\
    \to 19x > 3\\
    \to x > \dfrac{3}{{19}}\\
   2){x^2} < {x^2} + 4x + 4\\
    \to 4x >  – 4\\
    \to x >  – 1\\
   3)3 – \dfrac{{4x – 1}}{{18}} > \dfrac{{x – 1}}{{12}} – \dfrac{{4 – 5x}}{9}\\
    \to \dfrac{{3.36 – 2\left( {4x – 1} \right)}}{{36}} > \dfrac{{3\left( {x – 1} \right) – 4\left( {4 – 5x} \right)}}{{36}}\\
    \to 108 – 8x + 2 > 3x – 3 – 16 + 20x\\
    \to 31x < 129\\
    \to x < \dfrac{{129}}{{31}}\\
   4)\left( {2x – 3} \right)\left( {x + 3} \right) \ge 0\\
    \to \left[ \begin{array}{l}
   x \ge \dfrac{3}{2}\\
   x \le  – 3
   \end{array} \right.\\
   5)\dfrac{{3x – 1}}{4} – \dfrac{{3\left( {x – 2} \right)}}{8} – 1 > \dfrac{{5 – 3x}}{2}\\
    \to 2\left( {3x – 1} \right) – 3x + 6 – 8 > 4\left( {5 – 3x} \right)\\
    \to 6x – 2 – 3x – 2 > 20 – 12x\\
    \to 15x > 24\\
    \to x > \dfrac{8}{5}
   \end{array}\)

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2. `\text{~~Holi~~}`

   `1.`

   `x^3-6x^2-7x-5<(x-2)^3`

   `-> x^2-6x^2-7x-5<x^3-6x^2+12x-8`

   `-> -7x-5<12x-8`

   `-> -7x-12x<-8+5`

   `-> -19x<-3`

   `-> x>3/(19)`

   `2.`

   `x^2<(x+2)^2`

   `-> x^2<x^2+4x+4`

   `-> 0<4x+4`

   `-> -4x<4`

   `-> x>-1`

   `3.`

   `3-\dfrac{4x-1}{18}>\dfrac{x-1}{12}-\dfrac{4-5x}{9}`

   `-> 108-2(4x-1)>3(x-1)-4(4-5x)`

   `-> 108-8x+2>3x-3-16+20x`

   `-> 110-8x>23x-19`

   `-> -8x-23x-19-110`

   `-> -31x> -129`

   `-> x<(129)/(31)`

   `4.`

   `(2x-3)(x+3)\ge0`

   `->`\(\left[ \begin{array}{l}\begin{cases}2x-3\ge0\\x+3\ge0\end{cases}\\\begin{cases}2x-3\le0\\x+3\le0\end{cases}\end{array} \right.\) 

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

   `->`\(\left[ \begin{array}{l}x\in[\dfrac{3}{2},+∞)\\x\in(-∞,-3]\end{array} \right.\) 

   `-> x\in∈(-∞,-3]∪[3/2,+∞)`

   `5.`

   `(3x-1)/4-(3(x-2))/8-1>(5-3x)/2`

   `-> (3x-1)/4-(3x-6)/8-1>(5-3x)/2`

   `-> 2(3x-1)-(3x-6)-8>4(5-3x)`

   `-> 6x-2-3x+6-8>2x-12x`

   `-> 3x-4>20-12x`

   `-> 3x+12x>20+4`

   `-> 15x>24`

   `-> x>8/5`

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