\(x^3+x^2+\dfrac{1}{3}x+\dfrac{1}{27}\)

\(=x^3+3\cdot\dfrac{1}{3}\cdot x^2+3\cdot\left(\dfrac{1}{3}\right)^2\cdot x+\left(\dfrac{1}{3}\right)^3\)

\(=\left(x+\dfrac{1}{3}\right)^3\)

=x^3+3*x^2*1/3+3*x*(1/3)^2+(1/3)^3

=(x+1/3)^3

c: \(\Leftrightarrow2x+1=3\)

hay x=1

\(54-9\left(x+2\right)=27\\ \Rightarrow9\left(x+2\right)=27\\ \Rightarrow x+2=3\\ \Rightarrow x=1\)

`9x^2+6x-8=0`

`<=> 9x^2+12x-6x-8=0`

`<=> 3x(3x+4) - 2(3x+4)=0`

`<=>(3x+4)(3x-2)=0`

`<=> 3x+4=0` hoặc `3x-2=0`

`<=> 3x=-4` hoặc `3x=2`

`<=>x=-4/3` hoặc `x=2/3`

__

`2x^2 +3x-27=0`

`<=> 2x^2+9x-6x-27=0`

`<=>x(2x+9) - 3(2x+9)=0`

`<=> (2x+9)(x-3)=0`

`<=> 2x+9=0` hoặc `x-3=0`

`<=> 2x=-9` hoặc `x=3`

`<=>x=-9/2` hoặc `x=3`

=2/9

2/9

2/9

c) \(x^6-3x^4y+3x^2y^2-y^3\)

\(=\left(x^2\right)^3-3\cdot\left(x^2\right)^2\cdot y+3\cdot x^2\cdot y^2-y^3\)

\(=\left(x^2-y\right)^3\)

d) \(\left(x-y\right)^3+\left(x-y\right)^2+\dfrac{1}{2}\left(x-y\right)+\dfrac{1}{27}\)

\(=\left(x-y\right)^3+3\cdot\dfrac{1}{3}\cdot\left(x-y\right)^2+3\cdot\left(\dfrac{1}{3}\right)^2\cdot\left(x-y\right)+\left(\dfrac{1}{3}\right)^3\)

\(=\left(x-y+\dfrac{1}{3}\right)^3\)

giúp mình với mọi người ơi

\(\dfrac{8}{24}-\dfrac{5}{25}=\dfrac{1}{3}-\dfrac{1}{5}=\dfrac{5}{15}-\dfrac{3}{15}=\dfrac{2}{15}\\ \dfrac{18}{21}-\dfrac{12}{27}=\dfrac{6}{7}-\dfrac{4}{9}=\dfrac{54}{63}-\dfrac{28}{63}=\dfrac{26}{63}\)

1/3-1/5= 2/15

6/7-4/9= 26/63

a: \(\dfrac{x}{6}=\dfrac{8}{3}\)

=>\(x=6\cdot\dfrac{8}{3}=\dfrac{6}{3}\cdot8=8\cdot2=16\)

b: \(\dfrac{5}{x}=\dfrac{4}{9}\)

=>\(x=\dfrac{5\cdot9}{4}=\dfrac{45}{4}\)

c: \(\dfrac{x+3}{-4}=\dfrac{5}{20}\)

=>\(x+3=\dfrac{-4\cdot5}{20}=-1\)

=>x=-1-3=-4

d: \(\dfrac{7}{3+4x}=\dfrac{-2}{9}\)

=>\(4x+3=\dfrac{9\cdot7}{-2}=-\dfrac{63}{2}\)

=>\(4x=-\dfrac{63}{2}-3=-\dfrac{69}{2}\)

=>\(x=-\dfrac{69}{8}\)

f: ĐKXĐ: x<>1

\(\dfrac{3}{x-1}=\dfrac{x-1}{27}\)

=>\(\left(x-1\right)^2=3\cdot27=81\)

=>\(\left[{}\begin{matrix}x-1=9\\x-1=-9\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=10\left(nhận\right)\\x=-8\left(nhận\right)\end{matrix}\right.\)

cặp (x;y)(x;y) cần tìm là (1;31);(15;3);(−14;1);(0;−27)