e: \(\left\{{}\begin{matrix}\dfrac{1}{x}-\dfrac{1}{y}=1\\\dfrac{3}{x}+\dfrac{4}{y}=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{3}{y}=3\\\dfrac{3}{x}+\dfrac{4}{y}=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{-7}{y}=-2\\\dfrac{1}{x}-\dfrac{1}{y}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{7}{2}\\\dfrac{1}{x}=1+\dfrac{2}{7}=\dfrac{9}{7}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{7}{2}\\x=\dfrac{7}{9}\end{matrix}\right.\)

c) \(\left\{{}\begin{matrix}2\left(x-2\right)+3\left(1+y\right)=2\\3\left(x-2\right)-2\left(1+y\right)=-3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}6\left(x-2\right)+9\left(1+y\right)=6\\6\left(x-2\right)-4\left(1+y\right)=-6\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}13\left(1+y\right)=12\\2\left(x-2\right)+3\left(1+y\right)=2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{21}{13}\\y=-\dfrac{1}{13}\end{matrix}\right.\)

d) \(\left\{{}\begin{matrix}\left(x-5\right)\left(y-2\right)=\left(x+2\right)\left(y-1\right)\\\left(x-4\right)\left(y+7\right)=\left(x-3\right)\left(y+4\right)\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}xy-2x-5y+10=xy-x+2y-2\\xy+7x-4y-28=xy+4x-3y-12\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}-x-7y=-12\\3x-y=16\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}-x-7y=-12\\21x-7y=112\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}22x=124\\3x-y=16\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{62}{11}\\y=\dfrac{10}{11}\end{matrix}\right.\)

\(\left\{{}\begin{matrix}\left(x-5\right)\left(y-2\right)=\left(x+2\right)\left(y-1\right)\\\left(x-4\right)\left(y+7\right)=\left(x-3\right)\left(y+4\right)\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}xy-2x-5y+10=xy-x+2y-2\\xy+7x-4y-28=xy+4x-3y-12\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+7y=12\\3x-y=16\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}3x+21y=36\\3x-y=16\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}22y=20\\x+7y=12\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{62}{11}\\y=\dfrac{10}{11}\end{matrix}\right.\)

a: \(\left\{{}\begin{matrix}x+4y=-11\\5x-4y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x=-10\\x+4y=-11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-5}{3}\\y=\dfrac{-11-x}{4}=\dfrac{-11+\dfrac{5}{3}}{4}=-\dfrac{7}{3}\end{matrix}\right.\)

b: \(\left\{{}\begin{matrix}2x-y=7\\3x+5y=-22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-3y=21\\6x+15y=-66\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}-18y=78\\2x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{-13}{3}\\x=\dfrac{y+7}{2}=\dfrac{4}{3}\end{matrix}\right.\)

1.   3x( x - 2 ) - ( x - 2 ) = 0

<=> ( x-2).(3x-1)  = 0 => x = 2 hoặc x = \(\dfrac{1}{3}\)

2.    x( x-1 ) ( x² + x + 1 ) - 4( x - 1 )

<=> ( x - 1 ).( x (x^2 + x + 1 ) - 4 ) = 0

(phần này tui giải được x = 1 thôi còn bên kia giải ko ra nha )

3 \(\left\{{}\begin{matrix}\sqrt{5}x-2y=7\\\sqrt{5}x-5y=10\end{matrix}\right.\)<=> \(\left\{{}\begin{matrix}y=-1\\x=\sqrt{5}\end{matrix}\right.\)

\(1. 3x^2 - 7x +2=0\)

=>\(Δ=(-7)^2 - 4.3.2\)

        \(= 49-24 = 25\)

Vì 25>0 suy ra phương trình có 2 nghiệm phân biệt:

\(x_1\)=\(\dfrac{-\left(-7\right)+\sqrt{25}}{2.3}=\dfrac{7+5}{6}=2\)

\(x_2\)=\(\dfrac{-\left(-7\right)-\sqrt{25}}{2.3}=\dfrac{7-5}{6}=\dfrac{1}{3}\)

Bài 2: 

Ta có: \(A=\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{5}}-\sqrt{2}\)

\(=\dfrac{\sqrt{6+2\sqrt{5}}+\sqrt{14-6\sqrt{5}}-2}{\sqrt{2}}\)

\(=\dfrac{\sqrt{5}+1+3-\sqrt{5}-2}{\sqrt{2}}=\sqrt{2}\)

h) \(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=2\\\dfrac{3}{x}-\dfrac{4}{y}=-1\end{matrix}\right.\)\(\left(1\right)\)\(\left(đk:x,y\ne0\right)\)

Đặt \(a=\dfrac{1}{x},b=\dfrac{1}{y}\)

\(\left(1\right)\Leftrightarrow\) \(\left\{{}\begin{matrix}a+b=2\\3a-4b=-1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}3a+3b=6\\3a-4b=-1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a+b=2\\7b=7\end{matrix}\right.\)\(\Leftrightarrow a=b=1\)

Thay a,b:

\(\Leftrightarrow\dfrac{1}{x}=\dfrac{1}{y}=1\Leftrightarrow x=y=1\left(tm\right)\)

Ta có hệ \(\hept{\begin{cases}\left(4x^2+1\right)x+\left(y-3\right)\sqrt{5-2y}=0\left(1\right)\\4x^2+y^2+2\sqrt{3-4x}=7\left(2\right)\end{cases}}\)

ĐK \(\hept{\begin{cases}y\ge\frac{5}{2}\\x\le\frac{3}{4}\end{cases}}\)

Đặt \(\hept{\begin{cases}2x=a\\\sqrt{5-2y}=b\ge0\end{cases}\Rightarrow\hept{\begin{cases}4x^2=a^2\\5-2y=b^2\end{cases}}}\)\(\Rightarrow\hept{\begin{cases}4x^2=a^2\\y-3=\frac{5-b^2}{2}-3=\frac{-1-b^2}{2}\end{cases}}\)

Thế vào (1) ta có \(\left(a^2+1\right)\frac{a}{2}+\frac{-1-b^2}{2}b=0\)

\(\Leftrightarrow\frac{a^3+a}{2}+\frac{-b^3-b}{2}=0\Leftrightarrow a^3-b^3+a-b=0\)

\(\Leftrightarrow\left(a-b\right)\left(a^2+ab+b^2+1\right)=0\)

\(\Leftrightarrow a=b\)vì \(a^2+ab+b^2+1>0\forall a,b\)

\(\Rightarrow2x=\sqrt{5-2y}\Rightarrow4x^2=5-2y\Rightarrow y=\frac{5-4x^2}{2}\)

Thế y vào (2) ta có \(4x^2+\left(\frac{5-4x^2}{2}\right)^2+2.\sqrt{3-4x}=7\)

\(\Leftrightarrow16x^2+\left(5-4x^2\right)^2+8\sqrt{3-4x}=28\)\(\Leftrightarrow16x^2+25-40x^2+16x^4+8\sqrt{3-4x}-28=0\)

\(\Leftrightarrow16x^4-24x^2+8\sqrt{3-4x}-3=0\)

\(\Leftrightarrow\left(16x^4-1\right)-\left(24x^2-6\right)+\left(8\sqrt{3-4x}-8\right)=0\)

\(\Leftrightarrow\left(4x^2-1\right)\left(4x^2+1\right)-6\left(4x^2-1\right)+\left(8\sqrt{3-4x}-8\right)=0\)

\(\Leftrightarrow\left(4x^2-1\right)\left(4x^2+1\right)-6\left(4x^2-1\right)+8.\frac{2-4x}{\sqrt{3-4x}+1}=0\)

\(\Leftrightarrow\left(2x+1\right)\left(2x-1\right)\left(4x^2+1\right)-6\left(2x+1\right)\left(2x-1\right)-8.2.\frac{2x-1}{\sqrt{3-4x}+1}=0\)

\(\Leftrightarrow\left(2x-1\right)\left[\left(2x+1\right)\left(4x^2+1\right)-6\left(2x+1\right)-\frac{16.1}{\sqrt{3-4x}+1}\right]=0\)

\(\Leftrightarrow\left(2x-1\right)\left[\left(2x+1\right)\left(4x^2-5\right)-\frac{16}{\sqrt{3-4x}+1}\right]=0\)

\(\Leftrightarrow2x-1=0\)

Vì với \(y=\frac{5-4x^2}{2}\ge\frac{5}{2}\Rightarrow4x^2-5< 0\Rightarrow\left(2x+1\right)\left(4x^2-5\right)-\frac{16}{\sqrt{3-4x}+1}< 0\)

\(\Leftrightarrow x=\frac{1}{2}\Rightarrow y=\frac{5-4\left(\frac{1}{2}\right)^2}{2}=2\)

Vậy hệ có nghiệm \(\left(x;y\right)=\left(\frac{1}{2};2\right)\)