`x^4 -4sqr{3} -5 =0`

`<=> x^4 = 5 +4sqrt{3}`

`<=> x = +- root{4}{5+4sqrt(3)}`

Vậy `S ={ +- root{4}{5+4sqrt(3)} }`

a)

\(x^2-4\sqrt{15}x+19=0\\ < =>x^2-4\sqrt{15}x+60-41=0\\ < =>\left(x-2\sqrt{15}\right)^2-41=0\\ < =>\left(x-2\sqrt{15}-\sqrt{41}\right)\left(x-2\sqrt{15}+\sqrt{41}\right)=0\\ < =>\left[{}\begin{matrix}x-2\sqrt{15}-\sqrt{41}=0\\x-2\sqrt{15}+\sqrt{41}=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=2\sqrt{15}+\sqrt{41}\\x=2\sqrt{15}-\sqrt{41}\end{matrix}\right.\)

b)

\(4x^2+4\sqrt{5}x+5=0\\ < =>\left(2x+\sqrt{5}\right)^2=0\\ < =>2x+\sqrt{5}=0\\ < =>2x=-\sqrt{5}\\ < =>-\dfrac{\sqrt{5}}{2}\)

a: Δ=(4căn 15)^2-4*1*19=164>0

Phương trình có hai nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x=\dfrac{4\sqrt{5}-2\sqrt{41}}{2}=2\sqrt{5}-\sqrt{41}\\x_2=2\sqrt{5}+\sqrt{41}\end{matrix}\right.\)

b: \(\Leftrightarrow\left(2x\right)^2+2\cdot2x\cdot\sqrt{5}+5=0\)

=>(2x+căn 5)^2=0

=>2x+căn 5=0

=>x=-1/2*căn 5

\(\left(4-3x\right)\left(10x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}4-3x=0\\10x-5=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=\dfrac{1}{2}\end{matrix}\right.\)

\(S=\left\{\dfrac{4}{3},\dfrac{1}{2}\right\}\)

Ta có: \(\left(4-3x\right)\left(10x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}4-3x=0\\10x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=4\\10x=5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=\dfrac{1}{2}\end{matrix}\right.\)

Vậy: \(S=\left\{\dfrac{4}{3};\dfrac{1}{2}\right\}\)

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:

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

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

\(\left(2x+5\right)\left(x-4\right)+3\left(x-4\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(\left(2x+5\right)+3\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(2x+5+3\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(2x+8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\2x+8=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\2x=-8\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{8}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

\(\left(2x+5\right)\left(x-4\right)+3\left(x-4\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left[\left(2x+5\right)+3\right]=0\)

\(\Leftrightarrow\left(x-4\right)\left(2x+8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\2x+8=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

\(4x^2-4x-5\left|2x-1\right|-5=0\)

\(\Leftrightarrow-5\left|2x-1\right|=5-4x^2+4x\)

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

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

TH1 : \(2x-1=\frac{4x\left(x-1\right)}{5}-1\Leftrightarrow2x=\frac{4x\left(x-1\right)}{5}\)

\(\Leftrightarrow10x=4x^2-4x\Leftrightarrow14x-4x^2=0\)

\(\Leftrightarrow-2x\left(2x-7\right)=0\Leftrightarrow x=0;x=\frac{7}{2}\)

TH2 : \(2x-1=-\left(\frac{4x\left(x-1\right)}{5}-1\right)\Leftrightarrow2x-1=-\frac{4x\left(x-2\right)}{5}+1\)

\(\Leftrightarrow2x-2=-\frac{4x\left(x-2\right)}{5}\Leftrightarrow10x-10=-4x^2+8x\)

\(\Leftrightarrow2x-10+4x^2=0\Leftrightarrow2\left(2x^2+x-5\ne0\right)=0\)tự chứng minh 

Vậy tập nghiệm của phương trình là S = { 0 ; 7/2 }