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

\(f\left(x\right)< 0,\forall x\in R\Leftrightarrow\left\{{}\begin{matrix}a< 0\\\Delta< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m-4< 0\\\left(m+1\right)^2-4\left(m-4\right)\left(2m-1\right)< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m< 4\\m^2+2m+1-4\left(2m^2-m-8m+4\right)< 0\end{matrix}\right.\)

\(\Leftrightarrow m^2+2m+1-8m^2+36m-16< 0\)

\(\Leftrightarrow-7m^2+38m-15< 0\)

\(\Leftrightarrow\left\{{}\begin{matrix}m< 4\\\left[{}\begin{matrix}m< \dfrac{3}{7}\\m>5\end{matrix}\right.\end{matrix}\right.\)

\(KL:m\in\left(5;+\infty\right)\)

A, m x 3 + m x 7 = 1530
    m x (3+7)       = 1530
    m x 10            = 1530
⇒ m = 153
 B, m x 13 - 4 x m = 918
     m x (13-4)       = 918
     m x 9               = 918
⇒ m = 102
 

a) m x (3+7)=1530

m x 10=1530

m=1530/10

m=153

b)m x (13-4)=918

m x 9=918

m=918/9

m=102

=> m⁴ = 16m⁴

m⁴ - 16m⁴ = 0

m⁴.(1 - 16) = 0

m⁴.(-15) = 0

m⁴ = 0 : (-15)

m⁴ = 0

<=> m = 0

ĐKXĐ: x∉{0;-1}

\(\frac{x+m}{x+1}+\frac{x-2}{x}=2\)

=>\(\frac{x\left(x+m\right)+\left(x-2\right)\left(x+1\right)}{x\left(x+1\right)}=2\)

=>x(x+m)+(x-2)(x+1)=2x(x+1)

=>\(x^2+mx+x^2-x-2=2x^2+2x\)

=>x(m-1)-2=2x

=>x(m-1)-2x=2

=>x(m-3)=2

Để phương trình vô nghiệm thì \(\left[\begin{array}{l}m-3=0\\ \frac{2}{m-3}=-1\\ \frac{2}{m-3}=0\end{array}\right.\Rightarrow\left[\begin{array}{l}m=3\\ m-3=-2\end{array}\right.\Rightarrow\left[\begin{array}{l}m=3\\ m=1\end{array}\right.\)

=>Chọn A

ĐKXĐ: x∉{0;-1}

\(\frac{x+m}{x+1}+\frac{x-2}{x}=2\)

=>\(\frac{x\left(x+m\right)+\left(x-2\right)\left(x+1\right)}{x\left(x+1\right)}=2\)

=>x(x+m)+(x-2)(x+1)=2x(x+1)

=>\(x^2+mx+x^2-x-2=2x^2+2x\)

=>x(m-1)-2=2x

=>x(m-1)-2x=2

=>x(m-3)=2

Để phương trình vô nghiệm thì \(\left[\begin{array}{l}m-3=0\\ \frac{2}{m-3}=-1\\ \frac{2}{m-3}=0\end{array}\right.\Rightarrow\left[\begin{array}{l}m=3\\ m-3=-2\end{array}\right.\Rightarrow\left[\begin{array}{l}m=3\\ m=1\end{array}\right.\)

=>Chọn A

Vì hai bài giống nhau nên anh sẽ làm mẫu bài 1 nhé.