phân tích các số sau ra thừa số nguyên tố 48;56;84;105;360

=>10x+15y=5m và -10x+2y=-2

=>17y=5m-2 và -5x+y=-1

=>y=5/17m-2/17 và 5x-y=1

=>y=5/17m-2/17 và 5x=1+y=5/17m+15/17

=>y=5/17m-2/17 và x=1/17m+5/17

x>0; y>0

=>5m-2>0 và m+5>0

=>m>2/5

a, 117 - \(x\) = 28 - (-7)

   117 - \(x\) = 28 + 7

    117 - \(x\) = 35

            \(x\) =  117 - 35

             \(x\) = 82

b, \(x\) - (-38 - 2\(x\)) = (-3) - 8 + 2\(x\) 

    \(x\) + 38 + 2\(x\) = - 11 + 2\(x\)

   3\(x\)  + 38       = - 11 + 2\(x\)

   3\(x\) - 2\(x\)        = - 11 - 38

   \(x\)                = - 49

a) \(\text{5x(x-2)+(2-x)=0}\)

\(\Rightarrow5x\left(x-2\right)-\left(x-2\right)=0\\ \Rightarrow\left(x-2\right)\left(5x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\5x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{5}\end{matrix}\right.\)

b) \(\text{x(2x-5)-10x+25=0}\)

\(\Rightarrow x\left(2x-5\right)-5\left(2x-5\right)=0\\ \Rightarrow\left(x-5\right)\left(2x-5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\2x-5=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x=2,5\end{matrix}\right.\)

c) \(\dfrac{25}{16}-4x^2+4x-1=0\)

\(\Rightarrow\dfrac{9}{16}-4x^2+4x=0\)

\(\Rightarrow-4x^2+4x+\dfrac{9}{16}=0\)

\(\Rightarrow-4x^2-\dfrac{1}{2}x+\dfrac{9}{2}x+\dfrac{9}{16}=0\)

\(\Rightarrow\left(-4x^2-\dfrac{1}{2}x\right)+\left(\dfrac{9}{2}x+\dfrac{9}{16}\right)=0\)

\(\Rightarrow-\dfrac{1}{2}x\left(8x+1\right)+\dfrac{9}{16}\left(8x+1\right)=0\)

\(\Rightarrow\left(-\dfrac{1}{2}x+\dfrac{9}{16}\right)\left(8x+1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}-\dfrac{1}{2}x+\dfrac{9}{16}=0\\8x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{9}{8}\\x=\dfrac{-1}{8}\end{matrix}\right.\)

a) \(5x\left(x-2\right)+\left(2-x\right)=0\)

\(\Rightarrow5x\left(x-2\right)-\left(x-2\right)=0\)

\(\Rightarrow\left(x-2\right)\left(5x-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-2=0\\5x-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{5}\end{matrix}\right.\)

b) \(x\left(2x-5\right)-10x+25=0\)

\(\Rightarrow x\left(2x-5\right)-5\left(2x-5\right)=0\)

\(\Rightarrow\left(x-5\right)\left(2x-5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-5=0\\2x-5=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{5}{2}\end{matrix}\right.\)

c) \(\dfrac{25}{16}-4x^2+4x-1=0\)

\(\Rightarrow-4x^2+4x+\dfrac{9}{16}=0\)

\(\Rightarrow\left(x-\dfrac{9}{8}\right)\left(x+\dfrac{1}{8}\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{9}{8}=0\\x+\dfrac{1}{8}=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{9}{8}\\x=-\dfrac{1}{8}\end{matrix}\right.\)

d) \(x^4+2x^2-8=0\)

\(\Rightarrow\left(x^4+2x^2+1\right)-9=0\)

\(\Rightarrow\left(x^2+1\right)^2-3^2=0\)

\(\Rightarrow\left(x^2+1-3\right)\left(x^2+1+3\right)=0\)

\(\Rightarrow\left(x^2-2\right)\left(x^2+4\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x^2-2=0\\x^2+4=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x^2=2\\x^2=-4\end{matrix}\right.\) \(\Rightarrow x^2=2\) \(\Rightarrow x=\pm\sqrt{2}\)

\(\Delta=\left(-5\right)^2-4\cdot2\cdot m=25-8m\)

\(f\left(x\right)\ge0\)

\(\Leftrightarrow\Delta\le0\)

\(\Leftrightarrow25-8m\le0\)

\(\Leftrightarrow m\ge\dfrac{25}{8}\)

C

c

a) \(3\frac{1}{3}\left(3\frac{1}{4}+2x\right)=6\frac{2}{3}\)

   \(3\frac{1}{3}\times3\frac{1}{4}+2x=6\frac{2}{3}\)

   \(10\frac{5}{6}+2x=6\frac{2}{3}\)

   \(2\times x=6\frac{2}{3}+10\frac{5}{6}=17,5\)

   \(x=17,5\div2=8,75\)

Vậy x = 8,75

b) \(x-25\%x=\frac{6}{11}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)\)

   \(x-\frac{25}{100}x=\frac{6}{11}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)\)

   \(x-\frac{1}{4}\times x=\frac{6}{11}\times1\frac{7}{12}=\frac{19}{22}\)

   \(x\times x=\frac{19}{22}+\frac{1}{4}=\frac{49}{44}\)

\(\Rightarrow2x\left(x\times x\right)=\frac{49}{44}\)   

   \(x=\frac{49}{44}\div2=\frac{49}{88}\)

   Vậy x = \(\frac{49}{88}\)

c) \(\left(4,5-2x\right)\times1\frac{4}{7}=\frac{11}{14}\)

   \(4,5-2x\times1\frac{4}{7}=\frac{11}{14}\)

   \(-2x\times1\frac{4}{7}=\frac{11}{14}-4,5=-3\frac{5}{7}\)

   \(-2\times x=-3\frac{5}{7}\div1\frac{4}{7}=-2\frac{4}{11}\)

   \(x=-2\frac{4}{11}\div\left(-2\right)=1\frac{2}{11}\)

Vậy x = \(1\frac{2}{11}\)

d) \(-3^2-|2x+3|=4\)

    \(9-|2x+3|=4\)

   \(-|2x+3|=4-9=-5\)

   \(-|2x|=-5-|3|=-8\)

   \(-|x|=-8\div2=-4\)

    \(-x=4\Rightarrow x=-4\)

   Vậy x = -4 (-x được xem là số đối của x)

\(8x-75=5x+21\)

\(8x-5x=75+21\)

\(3x=96\)

\(x=32\)

Vậy \(x=32.\)

\(9x+25=-\left(2x-58\right)\)

\(9x+25=-2x+58\)

\(9x+2x=-25+58\)

\(11x=33\)

\(x=3\)

Vậy \(x=3.\)

\(15-\left|2x-1\right|=-8\)

\(\left|2x-1\right|=23\)

\(\Rightarrow\orbr{\begin{cases}2x-1=23\\2x-1=-23\end{cases}\Rightarrow}\orbr{\begin{cases}2x=24\\2x=-22\end{cases}}\Rightarrow\orbr{\begin{cases}x=12\\x=-11\end{cases}}\)

Vậy \(x\in\left\{12;-11\right\}\)

8x-5x=75+21

3x=96

x=32

9x+25=-2x+58

9x+2x=58-25

11x=33

x=3

+)   (5x-1). (2x+3)-3. (3x-1)=0

10x^2+15x-2x-3 - 9x+3=0

10x^2 +8x=0

2x(5x+4)=0

=> x=0 hoặc x= -4/5

+)    x^3 (2x-3)-x^2 (4x^2-6x+2)=0

2x^4 -3x^3 -4x^4 + 6x^3 - 2x^2=0

-2x^4 + 3x^3-2x^2=0

x^2(-2x^2+x-2)=0

-2x^2(x-1)^2=0

=> x=0 hoặc x=1

+)   x (x-1)-x^2+2x=5

x^2 -x -x^2+2x=5

x=5

+)     8 (x-2)-2 (3x-4)=25

8x - 16-6x+8=25

2x=33

x=33/2

a, \(5^0=1\)

b, \(12.35+35.182-35.66\)

\(=35.\left(12+182-66\right)\)

\(=35.128\)

\(=4480\)

c, \(x+2x=6\)

\(x.1+2.x=6\)

\(x\left(1+2\right)=6\)

\(x.3=6\)

\(x=2\)

d, \(x+x=30\)

\(2x=30\)

\(x=30:2\)

\(x=15\)

e, 2x -25 +5x =45

2x+5x=45+25

2x + 5x = 70

7x = 70

x = 10

f, x-7 + 2x = 8

x+2x=8+7

3x =15

x = 5

\(15-\left(x-4\right)=8\)

\(x-4=15-8\)

\(x-4=7\)

\(x=7+4\)

\(x=11\)

x=11

x=9

x=-3

x=-3

x=7 hoặc x=-17

x=7 hoặc x=-6

\(14-\left(25-8\right)=x-\left(19-7\right)\)

\(14-17=x-12\)

\(x-12=-3\)

\(x=-3+12\)

\(x=9\)