Theo đề bài thì ta có:

\(\hept{\begin{cases}3x_1^2+5x_1+4-m=0\\x_2^2-5x_2+4+m=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}9x_1^2+15x_1+12-3m=0\left(1\right)\\x_2^2-5x_2+4+m=0\left(2\right)\end{cases}}\)

Lấy (1) - (2) ta được

\(\left(9x_1^2-x_2^2\right)+\left(15x_1+5x_2\right)+8-4m=0\)

\(\Leftrightarrow\left(3x_1+x_2\right)\left(3x_1-x_2+5\right)+8-4m=0\)

\(\Leftrightarrow\left(3x_1+x_2\right)\left(3x_1+x_2-2x_2+5\right)+8-4m=0\)

\(\Leftrightarrow\left(6-2x_2\right)+8-4m=0\)

\(\Leftrightarrow x_2=7-2m\)

Thế lại vô (2) ta được

\(\left(7-2m\right)^2-5\left(7-2m\right)+4+m=0\)

\(\Leftrightarrow4m^2-17m+18=0\)

\(\Leftrightarrow\orbr{\begin{cases}m=2\\m=\frac{9}{4}\end{cases}}\)

Oh thanks you very muck!!!!

a=1; b=-2m-2; c=-4

Vì ac<0

nên phương trình luôn có hai nghiệm phân biệt

Ptr có: `\Delta = b^2 - 4ac = [-(2m + 1)]^2 - 4 . (-4)`

                                         `= ( 2m + 1)^2 + 16 > 0 AA m`

    `=> \Delta > 0 AA m`

Vật ptr luôn có `2` nghiệm `x_1 , x_2` với mọi `m`

\(\dfrac{4}{7}-\dfrac{4}{9}\)

\(=\dfrac{36}{63}-\dfrac{28}{63}\)

\(=\dfrac{8}{63}\)

Hình như sai đề rồi

à mấy số đó là số mũ nha

x⁶- x⁵+x⁴ - x³ + x² -x +3/4 =0

cau dong nao di

ĐKXĐ: \(x\ne\left\{-3;-2;-1;0\right\}\)

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

\(\Leftrightarrow\dfrac{1}{x}-\dfrac{1}{x+1}+\dfrac{1}{x+1}-\dfrac{1}{x+2}+\dfrac{1}{x+2}-\dfrac{1}{x+3}=\dfrac{x}{x\left(x+3\right)}\)

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

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

\(\Leftrightarrow x=3\)

\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{6}\\\dfrac{\dfrac{2}{3}}{x}+\dfrac{\dfrac{2}{3}}{y}+\dfrac{\dfrac{8}{9}}{y}=1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{6}\\\dfrac{\dfrac{2}{3}}{x}+\dfrac{\dfrac{14}{9}}{y}=1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{6}\left(1\right)\\\dfrac{2}{3x}+\dfrac{14}{9y}=1\left(2\right)\end{matrix}\right.\)

Nhân cả hai vế (1) cho \(\dfrac{2}{3}\) ta có: \(\left\{{}\begin{matrix}\dfrac{2}{3x}+\dfrac{2}{3y}=\dfrac{5.2}{6.3}\\\dfrac{2}{3x}+\dfrac{14}{9y}=1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{3x}+\dfrac{2}{3y}=\dfrac{10}{18}\left(3\right)\\\dfrac{2}{3x}+\dfrac{14}{9y}=1\left(4\right)\end{matrix}\right.\)

Lấy (4) trừ (3) ta có:

\(\dfrac{14}{9y}-\dfrac{2}{3y}=1-\dfrac{10}{18}\)\(\Leftrightarrow\dfrac{8}{9y}=\dfrac{4}{9}\)\(\Leftrightarrow y=2\Rightarrow x=\dfrac{1}{\dfrac{5}{6}-\dfrac{1}{2}}=3\)

\(\dfrac{2x-2\sqrt{x}+2}{x\sqrt{x}+1}=\dfrac{2}{\sqrt{x}+1}\)

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