Bài 1:
$2x^4-3x^2-5=0$

$\Leftrightarrow (2x^4+2x^2)-(5x^2+5)=0$

$\Leftrightarrow 2x^2(x^2+1)-5(x^2+1)=0$
$\Leftrightarrow (x^2+1)(2x^2-5)=0$

$\Leftrightarrow 2x^2-5=0$ (do $x^2+1\geq 1>0$ với mọi $x\in\mathbb{R}$)

$\Leftrightarrow x^2=\frac{5}{2}$

$\Leftrightarrow x=\pm \sqrt{\frac{5}{2}}$

Bài 2:

a. Khi $m=1$ thì pt trở thành:

$x^2-6x+5=0$

$\Leftrightarrow (x^2-x)-(5x-5)=0$

$\Leftrightarrow x(x-1)-5(x-1)=0$
$\Leftrightarrow (x-1)(x-5)=0$
$\Leftrightarrow x-1=0$ hoặc $x-5=0$

$\Leftrightarrow x=1$ hoặc $x=5$

b.

Để pt có 2 nghiệm $x_1,x_2$ thì:
$\Delta=(m+5)^2-4(-m+6)\geq 0$

$\Leftrightarrow m^2+14m+1\geq 0(*)$

Áp dụng định lý Viet:

$x_1+x_2=m+5$
$x_1x_2=-m+6$

Khi đó:
$x_1^2x_2+x_1x_2^2=18$

$\Leftrightarrow x_1x_2(x_1+x_2)=18$

$\Leftrightarrow (m+5)(-m+6)=18$

$\Leftrightarrow -m^2+m+12=0$
$\Leftrightarrow m^2-m-12=0$

$\Leftrightarrow (m+3)(m-4)=0$

$\Leftrightarrow m=-3$ hoặc $m=4$

Thử lại vào $(*)$ thấy $m=4$ thỏa mãn.

a)2x-3=0

⇔2x=3

⇔x=3/2

a: \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x+1+1}{x+1}+\dfrac{2}{y-2}=6\\\dfrac{5}{x+1}-\dfrac{1}{y-2}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x+1}+\dfrac{2}{y-2}=5\\\dfrac{5}{x+1}-\dfrac{1}{y-2}=3\end{matrix}\right.\)

=>x+1=1 và y-2=1/2

=>x=0 và y=5/2

b: \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{x-2y}=\dfrac{1}{2}-\dfrac{1}{18}=\dfrac{9}{18}-\dfrac{1}{18}=\dfrac{8}{18}=\dfrac{4}{9}\\\dfrac{2}{2x-y}=\dfrac{1}{18}+\dfrac{1}{x-2y}\end{matrix}\right.\)

=>x-2y=9 và 2/2x-y=1/18+1/9=1/18+2/18=3/18=1/6

=>x-2y=9 và 2x-y=12

=>x=5; y=-2

c: \(\Leftrightarrow\left\{{}\begin{matrix}10\left|x-6\right|+15\left|y+1\right|=25\\10\left|x-6\right|-8\left|y+1\right|=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}23\left|y+1\right|=23\\\left|x-6\right|=1\end{matrix}\right.\)

=>|x-6|=1 và |y+1|=1

=>\(\left\{{}\begin{matrix}x\in\left\{7;5\right\}\\y\in\left\{0;-2\right\}\end{matrix}\right.\)

\(\frac{x+a}{x-5}+\frac{x+5}{x-a}=2\) ĐKXĐ: \(x\ne5\), \(x\ne a\)

\(\Leftrightarrow\frac{\left(x+a\right)\left(x-a\right)}{\left(x-5\right)\left(x-a\right)}+\frac{\left(x+5\right)\left(x-5\right)}{\left(x-5\right)\left(x-a\right)}=2\)\(\Leftrightarrow\frac{x^2-a^2+x^2-25}{\left(x-5\right)\left(x-a\right)}=2\)

\(\Leftrightarrow\frac{2x^2-a^2-25}{\left(x-5\right)\left(x-a\right)}=2\)\(\Leftrightarrow2x^2-a^2-25=2\left(x^2-ax-5x+5a\right)\)

\(\Leftrightarrow2x^2-a^2-25=2x^2-2ax-10x+10a\)

\(\Leftrightarrow-a^2+2ax-10a+10x-25=0\)\(\Leftrightarrow a^2-2ax+10a-10x+25=0\)

\(\Leftrightarrow a^2-2\left(x-5\right)a-10x+25=0\)\(\Leftrightarrow a^2-2\left(x-5\right)a+\left(x^2-10x+25\right)-x^2=0\)

\(\Leftrightarrow a^2-2\left(x-5\right)a+\left(x-5\right)^2=x^2\)\(\Leftrightarrow\left[a-\left(x-5\right)\right]^2=x^2\)

\(\Leftrightarrow\left(a-x+5\right)^2=x^2\)

\(\Leftrightarrow\orbr{\begin{cases}a-x+5=x\\a-x+5=-x\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}a+5=2x\\a+5=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=\frac{a+5}{2}\\a=-5\end{cases}}\)(đối chiếu ĐKXĐ)

\(\Rightarrow\orbr{\begin{cases}x=\frac{a+5}{2},a\ne5\\a=-5,x\ne\pm5\end{cases}}\)

Vậy..........

Chắc đề phải là tìm a nguyên chứ bạn?

\(\left\{{}\begin{matrix}\left(a+1\right)x-ay=5\\x+ay=a^2+4a\end{matrix}\right.\)

\(\Rightarrow\left(a+2\right)x=a^2+4a+5\)

- Với \(a=-2\) hệ vô nghiệm

- Với \(a\ne-2\Rightarrow x=\dfrac{a^2+4a+5}{a+2}=a+2+\dfrac{1}{a+2}\)

\(x\in Z\Rightarrow\dfrac{1}{a+2}\in Z\Rightarrow a+2=\left\{-1;1\right\}\)

\(\Rightarrow a=\left\{-3;-1\right\}\)

a. Với y = 2 ta được:

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

\(B=\dfrac{4x\left(x+5\right)}{2+2}\)

Ta có pt:

\(\dfrac{x+2}{1}+3=\dfrac{4x\left(x+5\right)}{4}\)

\(\Leftrightarrow\dfrac{4\left(x+2\right)}{4}+\dfrac{12}{4}=\dfrac{4x^2+20x}{4}\)

\(\Leftrightarrow4x+8+12=4x^2+20x\)

\(\Leftrightarrow4x+20=4x^2+20x\)

\(\Leftrightarrow-4x^2-16x+20=0\)

\(\Leftrightarrow4x^2+16x-20=0\)

\(\Leftrightarrow\left(4x^2-4x\right)+\left(20x-20\right)=0\)

\(\Leftrightarrow4x\left(x-1\right)+20\left(x-1\right)=0\)

\(\Leftrightarrow\left(4x+20\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=1\end{matrix}\right.\)

Vậy..........

\(a.\frac{4x-3}{x-5}=\frac{29}{3}\\ \Leftrightarrow\frac{3\left(4x-3\right)}{3\left(x-5\right)}=\frac{29\left(x-5\right)}{3\left(x-5\right)}\\ \Leftrightarrow3\left(4x-3\right)=29\left(x-5\right)\\ \Leftrightarrow3\left(4x-3\right)-29\left(x-5\right)=0\\ \Leftrightarrow12x-9-29x+145=0\\ \Leftrightarrow-17x+136=0\\ \Leftrightarrow-17x=-136\\ \Leftrightarrow x=\frac{-136}{-17}=8\)

\(b.\frac{2x-1}{5-3x}=2\\ \Leftrightarrow\frac{2x-1}{5-3x}=\frac{4}{2}\\ \Leftrightarrow\frac{2\left(2x-1\right)}{2\left(5-3x\right)}=\frac{4\left(5-3x\right)}{2\left(5-3x\right)}\\ \Leftrightarrow2\left(2x-1\right)=4\left(5-3x\right)\\ \Leftrightarrow2\left(2x-1\right)-4\left(5-3x\right)=0\\ \Leftrightarrow4x-2-20+12x=0\\ \Leftrightarrow16x-22=0\\ \Leftrightarrow16x=22\\ \Leftrightarrow x=\frac{22}{16}=\frac{11}{8}\)

\(c.\frac{4x-5}{x-1}=\frac{2+x}{x-1}\\ \Leftrightarrow4x-5=2+x\\ \Leftrightarrow4x-5-2-x=0\\ \Leftrightarrow3x-7=0\\ \Leftrightarrow3x=7\\ \Leftrightarrow x=\frac{7}{3}\)

\(d.\frac{7}{x+2}=\frac{3}{x-5}\\ \Leftrightarrow\frac{7\left(x-5\right)}{\left(x+2\right)\left(x-5\right)}=\frac{3\left(x+2\right)}{\left(x+2\right)\left(x-5\right)}\\ \Leftrightarrow7\left(x-5\right)=3\left(x+2\right)\\ \Leftrightarrow7\left(x-5\right)-3\left(x+2\right)=0\\ \Leftrightarrow7x-35-3x-6=0\\ \Leftrightarrow4x-41=0\\ \Leftrightarrow4x=41\\ \Leftrightarrow x=\frac{41}{4}\)

\(e.\frac{2x+5}{2x}-\frac{x}{x+5}=0\\ \Leftrightarrow\frac{\left(2x+5\right)\left(x+5\right)}{2x\left(x+5\right)}-\frac{x.2x}{2x\left(x+5\right)}=0\\ \Leftrightarrow\left(2x+5\right)\left(x+5\right)-2x^2=0\\ \Leftrightarrow2x^2+10x+5x+25-2x^2=0\\ \Leftrightarrow15x+25=0\\ \Leftrightarrow15x=-25\\ \Leftrightarrow x=\frac{-25}{15}=\frac{-5}{3}\)

\(f.\frac{12x+1}{11x-4}+\frac{10x-4}{9}=\frac{20x+17}{18}\\\Leftrightarrow\frac{18\left(12x+1\right)}{18\left(11x-4\right)}+\frac{\left(10x-4\right).2\left(11x-4\right)}{9.2\left(11x-4\right)}=\frac{\left(20x+17\right)\left(11x-4\right)}{18\left(11x-4\right)}\\ \Leftrightarrow18\left(12x+1\right)+\left(10x-4\right).2\left(11x-4\right)=\left(20x+17\right)\left(11x-4\right)\\ \Leftrightarrow220x^2+48x+50=220x^2+107x-68\\ \Leftrightarrow48x+50=107x-68\\ \Leftrightarrow48x-107x=-68-50\\ \Leftrightarrow59x=-118\\ \Leftrightarrow x=-2\)