Giúp mik với. Rút gọn: (x-3).(x+3).(x+2)-(x-1).(x^2-3)-5x(x+4)^2-(x-5)^2 Tìm x: (2x+3)^2+(x-1).(x+1)=5.(x+2)^2-(x-5).(x-1)+(x+4)^2

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1. Rút gọn:

   (x-3).(x+3).(x+2)-(x-1).(x^2-3)-5x(x+4)^2-(x-5)^2

   ⇔(x^2-9)(x+2)-(x-1).(x^2-3)-5x(x^2+8x+16)-(x^2-10x+25)

   ⇔x³-9x+2x²-18-x³+x²+3x-3-5x³-40x²-80x-x²+10x-25

   ⇔(x³-x³-5x³)+(2x²+x²-40x²-x²)+(-9x+3x-80x+10x)+(-18-3-25)

   ⇔-5x³-38x²-76x-46

   Tìm x:

   (2x+3)^2+(x-1).(x+1)=5.(x+2)^2-(x-5).(x-1)+(x+4)^2

   ⇔4x²+12x+9+x²-1=5x²+20x+20-x²+5x+x-5+x²+8x+16

   ⇔(4x²+x²-5x²+x²-x²)+(12x-20x-5x-x-8x)+(9-1-20+5-16)=0

   ⇔-22x=23

   ⇔x=-$\frac{23}{22}$

   S={ -$\frac{23}{22}$}

   Chúc bạn thi tốt

   Trả lời

2. `a, (x-3)(x+3)(x+2)-(x-1)(x^2-3)-5x(x+4)^2-(x-5)^2`

   `⇔ (x^2-9)(x+2)-(x^3-3x-x^2+3)-5x(x^2+8x+16)-(x^2-10x+25)`

   `⇔ x^3+2x^2-9x-18-x^3+3x+x^2-3-5x^3-40x^2-80x-x^2+10x-25`

   `⇔ -5x^3-38x^2-76x-46`

   `b, (2x+3)^2+(x-1)(x+1)=5(x+2)^2-(x-5)(x-1)+(x+4)^2`

   `⇔4x^2+12x+9+x^2-1=5(x^2+4x+4)-(x^2-x-5x+5)+x^2+8x+16`

   `⇔5x^2+12x+8=5x^2+20x+20-x^2+x+5x-5+x^2+8x+16`

   `⇔5x^2+12x+8-5x^2-20x-20+x^2-x-5x+5-x^2-8x-16=0`

   `⇔ -22x-23=0`

   `⇔-22x=23`

   `⇔x=-23/22`

   $\text{Vậy tập nghiệm của PT: S = {$\dfrac{-23}{22}$}}$

   Trả lời