\(\dfrac{5x+7}{10x-1}=\dfrac{2x+9}{4x-5}\)

\(\Rightarrow\left(5x+7\right)\left(4x-5\right)=\left(10x-1\right)\left(2x+9\right)\)

\(\Rightarrow20x^2+3x-35=20x^2+98x-9\)

\(\Rightarrow3x-35=98x-9\)

\(\Rightarrow-95x=26\)

\(\Rightarrow x=\dfrac{-26}{95}\)

Nếu còn tick cho nhau ở chủ đề này thì mình sẽ xóa nhé!

Mình thấy có nhiều bạn cũng giỏi mà vẫn chưa phải CTV, bạn cứ đăng câu hỏi thì sẽ có giải đáp, không được thì bạn cũng có thể đánh đề lên tra google ( có rất nhiều cách mà! )

Ta có: \(\dfrac{a}{b}< \dfrac{c}{d}\Rightarrow ad< bc\)

\(\Rightarrow ad+ab< bc+ab\)

\(\Rightarrow a\left(b+d\right)< b\left(a+c\right)\)

\(\Rightarrow\dfrac{a}{b}< \dfrac{a+c}{b+d}\)

\(\Rightarrowđpcm\)

a, \(\left(x-4\right)\left(x^2+4x+16\right)=x^3-64\)

b, \(\left(x-3\right)\left(x+3\right)\left(x^2+9\right)\)

\(=\left(x^2-9\right)\left(x^2+9\right)=x^4-81\)

c, \(\left(x^2+x-2\right)\left(x^2+x+2\right)\)

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

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

d, \(\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)=x^6-y^6\)

\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+3xyz\)

\(=\left[xy\left(x+y\right)+xyz\right]+\left[yz\left(y+z\right)+xyz\right]+\left[xz\left(x+z\right)+xyz\right]\)

\(=xy\left(x+y+z\right)+yz\left(x+y+z\right)+xz\left(x+y+z\right)\)

\(=\left(xy+yz+zx\right)\left(x+y+z\right)\)

\(A=\dfrac{1}{\left(-1997\right)\left(-1995\right)}+...+\dfrac{1}{\left(-3\right)\left(-1\right)}\)

\(=\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{1995.1997}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{1995.1997}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{1995}-\dfrac{1}{1997}\right)\)

\(=\dfrac{1}{2}.\dfrac{1996}{1997}=\dfrac{998}{1997}\)

+) Ta có: \(\dfrac{a}{b}< \dfrac{c}{d}\Rightarrow\dfrac{ad}{bd}< \dfrac{bc}{bd}\Rightarrow ad< bc\)

( do b, d > 0 )

+) Ta có: \(ad< bc\)

\(\Rightarrow\dfrac{ad}{bd}< \dfrac{bc}{bd}\Rightarrow\dfrac{a}{b}< \dfrac{c}{d}\left(b,d>0\right)\)

a, \(\left(3+xy^2\right)^2=9+x^2y^4+6xy^2\)

b, \(\left(10-2m^2n\right)^2\)

\(=100+40m^2n-4m^4n^2\)

c, \(\left(a-b^2\right)\left(a+b^2\right)=a^2-b^4\)

a, \(C=-\left|x+2\right|+4\le4\)

Dấu " = " khi \(-\left|x+2\right|=0\Rightarrow x=-2\)

Vậy MAX C = 4 khi x = -2

b, \(D=4,5-\left|x+2\right|\le4,5\)

Dấu " = " khi \(-\left|x+2\right|=0\Rightarrow x=-2\)

Vậy MAX D = 4,5 khi x = -2

\(3x-2⋮x+2\)

\(\Rightarrow3x+6-8⋮x+2\)

\(\Rightarrow3\left(x+2\right)-8⋮x+2\)

\(\Rightarrow8⋮x+2\)

\(\Rightarrow x+2\in\left\{1;-1;2;-2;4;-4;8;-8\right\}\)

\(\Rightarrow x\in\left\{-1;-3;0;-4;2;-6;6;-10\right\}\)

Vậy...