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a. (x + 2)(x2 – 3x + 5) = (x + 2)x2
⇔ (x + 2)(x2 – 3x + 5) – (x + 2)x2 = 0
⇔ (x + 2)[(x2 – 3x + 5) – x2] = 0
⇔ (x + 2)(\(x^2\) – 3x + 5 – \(x^2\)) = 0
⇔ (x + 2)(5 – 3x) = 0
⇔ x + 2 = 0 hoặc 5 – 3x = 0
x + 2 = 0 ⇔ x = -2
5 – 3x = 0 ⇔ x = \(\dfrac{5}{3}\)
Vậy phương trình có nghiệm x = -2 hoặc x =\(\dfrac{5}{3}\)
c.\(2x^2\) – x = 3 – 6x
⇔ \(2x^2\) – x + 6x – 3 = 0
⇔ (\(2x^2\) + 6x) – (x + 3) = 0
⇔ 2x(x + 3) – (x + 3) = 0
⇔ (2x – 1)(x + 3) = 0
⇔ 2x – 1 = 0 hoặc x + 3 = 0
2x – 1 = 0 ⇔ x = 1/2
x + 3 = 0 ⇔ x = -3
Vậy phương trình có nghiệm x = \(\dfrac{1}{2}\) hoặc x = -3
a)
\(\dfrac{x-3}{5}+\dfrac{1-2x}{3}=6\\ < =>3x-9+5-10x=90\)
\(< =>3x-10x=90+9-5\\ < =>-7x=94\\ < =>x=-\dfrac{94}{7}\)
b)
\(\left(2x-3\right)\left(x^2+1\right)=0\\ < =>\left[{}\begin{matrix}2x-3=0\\x^2+1=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=\dfrac{3}{2}\\x^2=-1\left(voli\right)\end{matrix}\right.\\ < =>x=\dfrac{3}{2}\)
c)
\(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\left(x\ne-1;x\ne2\right)\)
suy ra: \(2\left(x-2\right)-x-1=3x-11\)
\(< =>2x-4-x-1-3x+11=0\)
\(< =>2x-x-3x=4+1-11\\ < =>-2x=-6\\ < =>x=3\left(tm\right)\)
a) \(\dfrac{x-3}{5}+\dfrac{1-2x}{3}=6\)
\(\Leftrightarrow3\left(x-3\right)+5\left(1-2x\right)=90\)
\(\Leftrightarrow-4-7x=90\)
\(\Leftrightarrow x=-\dfrac{94}{7}\)
b) \(\left(2x-3\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow2x-3=0\) (Vì \(x^2+1>0\))
\(\Leftrightarrow x=\dfrac{3}{2}\)
c) \(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\left(Đk:x\ne-1;x\ne2\right)\)
\(\Leftrightarrow2\left(x-2\right)-\left(x+1\right)=3x-11\)
\(\Leftrightarrow x-5=3x-11\)
\(\Leftrightarrow x=3\)
a: \(\Leftrightarrow5x-2+\left(2x-1\right)\left(1-x\right)=2-2x-2x^2-2x+6\)
\(\Leftrightarrow5x-2+2x-2x^2-1+x=-2x^2-4x+8\)
=>8x-3=-4x+8
=>-4x=11
hay x=-11/4
b: \(\Leftrightarrow\left(-2x+5\right)\left(3x-1\right)+3\left(x^2-1\right)=\left(x+2\right)\left(1-3x\right)\)
\(\Leftrightarrow-6x^2+2x+15x-5+3x^2-3=x-3x^2+2-6x\)
\(\Leftrightarrow17x-8=-5x+2\)
=>22x=10
hay x=5/11
a) 4x -8 ≥ 3(3x-1)-2x +1
⇒4x -8 ≥7x -2
⇒4x -7x ≥ -2 +8
⇒-3x ≥ 6
⇒x≤-2
Vậy bpt có nghiệm là:{x|x≤-2}
b) (x-3)(x+2)+(x+4)2≤ 2x (x+5)+4
⇔ x2+2x - 3x - 6 +x2 + 8x +16≤ 2x2 + 10x +4
⇔ x2 +2x - 3x + x2 + 8x - 2x2- 10x ≤ 4+6-16
⇔ -3x ≤ -6
⇔ x≥ 2
Vậy bpt có tập nghiệm là: {x|x≥2}
a: \(\Leftrightarrow1-x+3x+3=2x+3\)
=>2x+4=2x+3(vô lý)
b: \(\Leftrightarrow\left(x+2\right)^2-2x+3=x^2+10\)
\(\Leftrightarrow x^2+4x+4-2x+3=x^2+10\)
=>4x+7=10
hay x=3/4
d: \(\Leftrightarrow\left(-2x+5\right)\left(3x-1\right)+3\left(x-1\right)\left(x+1\right)=\left(x+2\right)\left(1-3x\right)\)
\(\Leftrightarrow-6x^2+2x+15x-5+3\left(x^2-1\right)=\left(x+2\right)\left(1-3x\right)\)
\(\Leftrightarrow-6x^2+17x-5+3x^2-3=x-3x^2+2-6x\)
\(\Leftrightarrow-3x^2+17x-8=-3x^2-5x+2\)
=>22x=10
hay x=5/11
2.a)
\(2x\left(6x-1\right)>\left(3x-2\right)\left(4x+3\right)\)
\(\Leftrightarrow12x^2-2x>12x^2+9x-8x-6\)
\(\Leftrightarrow12x^2-2x-12x^2-9x+8x>6\)
\(\Leftrightarrow-3x>6\)
\(\Leftrightarrow3>\dfrac{6}{-3}\)
\(\Leftrightarrow x< -2\)
Vậy nghiệm của bpt \(S=\left\{-2\right\}\)
2.b)
\(\dfrac{2\left(x+1\right)}{3}-2\ge\dfrac{x-2}{2}\)
\(\Leftrightarrow4\left(x+1\right)-2.6\ge3x-6\)
\(\Leftrightarrow4x+4-12\ge3x-6\)
\(\Leftrightarrow4x-3x\ge-6-4+12\)
\(\Leftrightarrow x\ge2\)
vậy nghiệm của bpt x\(\ge\)2
a: \(\Leftrightarrow x^3-3x^2+3x-1-x^3+2x^2-x=5x\left(2-x\right)-11\left(x+2\right)\)
=>-x^2+2x-1=10x-5x^2-11x-22
=>-x^2+2x-1=-5x^2-x-22
=>4x^2+3x+21=0
=>PTVN
b: \(\Leftrightarrow\left(x+10\right)\left(x+4\right)+3\left(x+4\right)\left(x-2\right)=4\left(x+10\right)\left(x-2\right)\)
=>x^2+14x+40+3(x^2+2x-8)=4(x^2+8x-20)
=>x^2+14x+40+3x^2+6x-24=4x^2+32x-80
=>20x+16=32x-80
=>-12x=-96
=>x=8
c: \(\Leftrightarrow6\left(x-3\right)+7\left(x-5\right)=13x+4\)
=>6x-18+7x-35=13x+4
=>-53=4(loại)
d: =>3(2x-1)-5(x-2)=3(x+7)
=>6x-3-5x+10=3x+21
=>3x+21=x+7
=>x=-7
e: =>x^3-6x^2+12x-8-x^3-3x^2-3x-1=-9x^2+1
=>-9x^2+9x-9=-9x^2+1
=>9x=10
=>x=10/9
\(đkxđ:x\ne-1;x\ne2\)
\(\Leftrightarrow\dfrac{2\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}-\dfrac{1\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\\ \Leftrightarrow2x-4-x-1=3x-11\\ \Leftrightarrow2x-4-x-1-3x+11=0\\ \Leftrightarrow-2x+6=0\\ \Leftrightarrow-2x=-6\\ \Leftrightarrow x=3\)