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c: =>4(2x+2)+6>5(3x-2)
=>8x+8+6>15x-10
=>8x+14>15x-10
=>-7x>-24
hay x<24/7
d: =>3(2x+1)-5(2x-2)>225
=>6x+3-10x+10>225
=>-4x+13>225
=>-4x>212
hay x<-53
c) \(=\left(4x-3\right)^2-\left(9x^2-4\right)\)
\(=16x^2-24x+9-9x^2+4=7x^2-24x+13\)
d) \(=\left(x^2-3x+2\right)\left(x+3\right)-\left(x^3-5x^2\right)\)
\(=x^3+3x^2-3x^2-9x+2x+6-x^3+5x^2\)
\(=5x^2-7x+6\)
c. (4x - 3)(4x - 3) - (3x + 2)(3x - 2)
= (4x - 3)2 - (9x2 - 4)
= 16x2 - 24x + 9 - 9x2 + 4
= 16x2 - 9x2 - 24x + 9 + 4
= 7x2 - 24x + 13
d. (x - 2)(x - 1)(x + 3) - x2(x - 5)
= (x2 - 1 - 2x + 2)(x + 3) - x2(x - 5)
= x3 + 3x2 - x - 3 - 2x2 - 6x + 2x + 6 - x3 + 5
= x3 - x3 + 3x2 - 2x2 - x - 6x + 2x + 6 + 5 - 3
= x2 - 5x + 8
d) \(\dfrac{5x+2}{6}\) +\(\dfrac{3-4x}{2}\) = 2-\(\dfrac{x+7}{3}\)
=>5x+2+3(3-4x)=12-2(x+7)
5x+2+9-12x=12-2x-14
-5x=-13
x=\(\dfrac{13}{5}\)
e) \(\dfrac{-20}{9}x +4=\dfrac{8}{3}x-40\)
=>-20x+36=24x-360
-44x=-396
x=9
f) 3x(2x-5)-4X+10=0
6X2 -15X-4X+10=0
2x(3x-2)-5(3x-2)=0
(3x-2)(2x-5)=0
\(\left[\begin{array}{} Biểu thức (3x-2=0)\\ Biểu thức (2x-5=0) \end{array} \right.\)\(\left[\begin{array}{} (x=\dfrac{2}{3})\\ (x=\dfrac{5}{2}) \end{array} \right.\)
j) \(\dfrac{x-45}{55}+\dfrac{x-47}{53}=\dfrac{x-55}{45}+\dfrac{x-53}{47}\)
\(\dfrac{x-45}{55}-1+\dfrac{x-47}{53}-1=\dfrac{x-55}{45}-1+\dfrac{x-53}{47}-1\)
\(\dfrac{x-100}{55}+\dfrac{x-100}{53}=\dfrac{x-100}{45}+\dfrac{x-100}{47}\)
\(\dfrac{x-100}{55}+\dfrac{x-100}{53}-\dfrac{x-100}{45}-\dfrac{x-100}{47}=0\)
(x-100)(\(\dfrac{1}{55}+\dfrac{1}{53}-\dfrac{1}{45}-\dfrac{1}{47}\))=0
=> x-100=0(\(\dfrac{1}{55}+\dfrac{1}{53}-\dfrac{1}{45}-\dfrac{1}{47}\) >0)
=> x= 100
c: ΔABD đồng dạng với ΔACE
=>BD/CE=AB/AC
=>AB/AC=BM/CN
Xét ΔABM và ΔACN có
AB/AC=BM/CN
góc ABM=góc ACN
=>ΔABM đồng dạng với ΔACN
=>góc BAM=góc CAN
góc BAM+góc MAK=góc BAK
góc CAN+góc NAK=góc CAK
mà góc BAM=góc CAN và góc MAK=góc NAK
nên góc BAK=góc CAK
=>AK là phân giác của góc BAC
=>KB/AB=KC/AC
=>KB*AC=KC*AB
c) \(\left|x^2-2x-3\right|+\left|x+1\right|=0\)
\(\Leftrightarrow\left|\left(x+1\right)\left(x-3\right)\right|+\left|x+1\right|=0\)
\(\Leftrightarrow\left|x+1\right|.\left(\left|x-3\right|+1\right)=0\)
\(\Leftrightarrow\left|x+1\right|=0\) ( Do \(\left|x-3\right|+1>0\) )
\(\Leftrightarrow x=-1\)
Vậy $x=-1$
c) -△BKM∼△BHA (g-g) \(\Rightarrow\dfrac{BK}{BH}=\dfrac{BM}{BA}\)
\(\Rightarrow\)△BKH∼△BMA (c-g-c) \(\Rightarrow\dfrac{S_{BKH}}{S_{BMA}}=\left(\dfrac{BH}{BA}\right)^2=\left(\dfrac{\dfrac{2}{3}AB}{AB}\right)^2=\left(\dfrac{2}{3}\right)^2=\dfrac{4}{9}\)
\(\Rightarrow S_{BMA}=\dfrac{9}{4}.S_{BKH}=\dfrac{9}{4}.54=121,5\left(cm^2\right)\)
Bài 4. c)
\(P\left(x\right)=x^3+3x^2+mx+8\) chia hết cho \(x+4\) suy ra \(P\left(-4\right)=0\)
khi đó \(\left(-4\right)^3+3.\left(-4\right)^2+m.\left(-4\right)+8=0\Leftrightarrow m=-2\).