\(x^4+10x^3+35x^2+50x+21=0\)

\(\Leftrightarrow\left(x^2+5x+3\right)\left(x^2+5x+7\right)=0\)

\(\Leftrightarrow\)\(x^2+5x+3=0\) hoặc  \(x^2+5x+7=0\)

\(x^2+5x+3=0\), giải ra ta được 2 nghiệm.

\(x^2+5x+7\ge\frac{3}{4}\), vô nghiệm.

Vậy phương trình có 2 nghiệm.

mình mới lớp 6 thôi sorry nhìu nha

ờ lần sau mà ko biết thì đừng spam :3

\(\text{ Dễ thấy: }120=2^3.3.5\)

\(\text{ Ta có: }x^5+10x^4+35x^3+50x^2+24x.\)

\(=x\left(x^4+10x^3+35x^2+50x+24\right)\)

\(=x\left[x^3\left(x+1\right)+9x^2\left(x+1\right)+26x\left(x+1\right)+24\left(x+1\right)\right]\)

\(=x\left(x+1\right)\left(x^3+9x^2+26x+24\right)\)

\(=x\left(x+1\right)\left[x^2\left(x+2\right)+7x\left(x+2\right)+12\left(x+2\right)\right]\)

\(=x\left(x+1\right)\left(x+2\right)\left(x^2+7x+12\right)\)

\(=x\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(\text{ lm hơi tắt thông cảm!!}\right)\)

\(\Rightarrow x\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)⋮2\)

\(\Rightarrow x\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)⋮3\)

\(\Rightarrow x\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)⋮4\)

\(\Rightarrow x\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)⋮5\)

Vì 2,3,5 là các số nguyên tố cùng nhau nên 

\(x\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)⋮2.3.4.5=120\)

a) \(\dfrac{3x-4}{2x+5}=\dfrac{3x+7}{2x-20}\left(đk:x\ne-\dfrac{5}{2},x\ne10\right)\)

\(\Rightarrow\left(3x-4\right)\left(2x-20\right)=\left(3x+7\right)\left(2x+5\right)\)

\(\Rightarrow6x^2-68x+80=6x^2+29x+35\)

\(\Rightarrow97x=45\Rightarrow x=\dfrac{45}{97}\)

b) \(\dfrac{10x-5}{7x+2}=\dfrac{50x+10}{35x-29}\left(đk:x\ne-\dfrac{2}{7},x\ne\dfrac{29}{35}\right)\)

\(\Rightarrow\left(10x-5\right)\left(35x-29\right)=\left(50x+10\right)\left(7x+2\right)\)

\(\Rightarrow350x^2-465x+145=350x^2+170x+20\)

\(\Rightarrow635x=125\Rightarrow x=\dfrac{25}{127}\)

4 nghiệm
-1; 2; 3; 6

https://h.vn/hoi-dap/question/238231.html?pos=815256

Thay \(x=2\) vào pt \(x^2-10x+m^2=0\)

\(\Leftrightarrow2^2-10.2+m^2=0\)

\(\Leftrightarrow4-20+m^2=0\)

\(\Leftrightarrow m^2=16\)

\(\Leftrightarrow m=\pm4\)

Vậy \(m=\pm4\) thì pt có 1 nghiệm bằng 2.

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