a, Có x/7=y/3

=> x+y/7+3 = 100/10 = 10

=>x=10. 7= 70

=>y=10.3 = 30

b, Có x/7=y/3

=>x-y/7-3= 50 / 4= 12,5

=>x=12,5 . 7 =87,5

=>y= 12,5 . 3 =37,5

c, Có x/7=y/3

=>2x-y/2.7-3= 22/11=2

=>x=2.7=14

=>y=2.3=6

1.

a,  \(x-14=3x+18\)                                                                       

\(\Rightarrow x-3x=18+14\)                                                                 

\(\Rightarrow-2x=32\Rightarrow x=\frac{32}{-2}=-16\)

b, \(\left(x+7\right).\left(x-9\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x+7=0\\x-9=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-7\\x=9\end{cases}}}\)

c, \(\left|2x-5\right|-7=22\)                                                                     

\(\Rightarrow\left|2x-5\right|=22+7\)

\(\Rightarrow\left|2x-5\right|=29\)

\(\Rightarrow\orbr{\begin{cases}2x+5=29\\2x-5=29\end{cases}}\Rightarrow\orbr{\begin{cases}2x=24\\2x=34\end{cases}\Rightarrow}\orbr{\begin{cases}x=12\\x=17\end{cases}}\)

d,  \(\left(\left|2x\right|-5\right)-7=22\)

\(\Rightarrow\left(\left|2x\right|-5\right)=29\)

\(\Rightarrow\left|2x\right|=29+5\Rightarrow\left|2x\right|=34\Rightarrow x=\pm17\)

e, \(\left|x+3\right|+\left|x+9\right|+\left|x+5\right|=4x\)

Vì \(\left|x+3\right|\ge0;\left|x+9\right|\ge0;\left|x+5\right|\ge0;4x\ge0\)

Nên \(\left|x+3\right|+\left|x+9\right|+\left|x+5\right|=4x\ge0\)

\(\Rightarrow\left|x+3\right|>0\Rightarrow\left|x+3\right|=x+3\)

     \(\left|x+9\right|>0\Rightarrow\left|x+9\right|=x+9\)

      \(\left|x+5\right|>0\Rightarrow\left|x+5\right|=x+5\)

Ta có : 

\(x+3+x+9+x+5=4x\)

\(\Rightarrow3x+\left(3+9+5\right)=4x\)

\(\Rightarrow4x-3x=17\)

\(\Rightarrow x=17\)

2. a , b sai đề bn 

c, \(\left(5x+1\right).\left(y-1\right)=4\)

\(\Rightarrow\left(5x+1\right).\left(y-1\right)\inƯ\left(4\right)\)

\(\text{ }Ư\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)

Ta có bảng sau : 

d, \(5xy-5x+y=5\)

\(\Rightarrow\left(5xy-5x\right)+y=5\)

\(\Rightarrow5x.\left(y-1\right)+y=5\)

\(\Rightarrow\left(5x+1\right).\left(y-1\right)=4\)

\(\Rightarrow\left(5x+1\right).\left(y-1\right)\inƯ\left(4\right)\)

\(Ư\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)

Ta có bảng sau : 

x - 14 = 3x + 18

x - 3x = 18 + 14

-2x= 32

x= 32 : (-2)

x=-16

1) \(a^2x^2-a^2y^2-b^2x^2+b^2y^2=a^2\left(x^2-y^2\right)-b^2\left(x^2-y^2\right)=\left(x^2-y^2\right)\left(a^2-b^2\right)=\left(x-y\right)\left(x+y\right)\left(a-b\right)\left(a+b\right)\)

2) \(x^2-2014x+2013=\left(x-1007\right)^2-1006^2=\left(x-1007-1006\right)\left(x-1007+1006\right)=\left(x-2013\right)\left(x-1\right)\)

3) \(x^2-y^2+12y-36=x^2-\left(y-6\right)^2=\left(x-y+6\right)\left(x+y-6\right)\)

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

5) \(16x^2-y^2=\left(4x-y\right)\left(4x+y\right)\)

6) \(6x^2-11x+3=6\left(x-\dfrac{11}{12}\right)^2-\dfrac{49}{24}=6\left[\left(x-\dfrac{11}{12}\right)^2-\dfrac{49}{144}\right]=6\left(x-\dfrac{11}{12}-\dfrac{7}{12}\right)\left(x-\dfrac{11}{12}+\dfrac{7}{12}\right)=6\left(x-\dfrac{3}{2}\right)\left(x-\dfrac{1}{3}\right)=\left(2x-3\right)\left(3x-1\right)\)

a , x(3-x)-y(y-2x)+y(y-2)-x(2y-x)

=3x-x²-y²+2xy+y²-2y-2xy+x²

=3x-(-x²+x²)+(2xy-2xy)-2y

=3x-2y

b,(x²-7)(x+2)-(2x-1)(x-14)+x(x²-2x-22)+35

=x³+2x²-7x-14-2x²+29x-14+x³-2x²-22x+35

=(x³+x³)+(2x²-2x²-2x²)-(-7x+29x-22x)-14-14+35

=2x³-2x²+7

c,(2x+y)(4x²-2xy+y²)-8x³-y³

=2xy²-4x²y+8x³+y³-2xy²+4x²y-8x³-y³

=(2xy²-2xy²)-(-4x²y+4x²y)+(8x³-8x³)+(y³-y³)

=0 

a: \(A=x^4y+x^2y^3+x^2y^3+y^5-x^4y-y^5\)

\(=2x^2y^3\)

b: \(=4x^2-y^2-100\)

\(=4\cdot\left(-25\right)^2-10^2-100\)

=400-200=200

\(B=\left(x-y\right)\left(x^3+x^2y+xy^2+y^3\right)-x^4+y^4\)

\(=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4-x^4+y^4\)

\(=0\)

\(C=\left(2-x\right)\left(1+2x\right)+\left(2x-1\right)\left(x-14\right)+x\left(x^2-2x-22\right)+35\)

\(=2+3x-2x^2+2x^2-29x+14+x^3-2x^2-22x+35\)

\(=x^3-2x^2-48x+51\)

Đề bài sai