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\(x^3-5x^2+8x-4=0\Leftrightarrow x^3-x^2-4x^2+4x+4x-4=0\Leftrightarrow x^2\left(x-1\right)-4x\left(x-1\right)+4\left(x-1\right)=0\Leftrightarrow\left(x^2-4x+4\right)\left(x-1\right)=0\Leftrightarrow\left(x-2\right)^2\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}\left(x-2\right)^2=0\\\left(x-1\right)=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x=1\left(tm\right)\end{matrix}\right..Vậy:x\in\left\{1;2\right\}\)
Bài 4:
a: \(=7xy\left(2-3-4\right)=-35xy\)
b: \(=\left(x-5\right)\left(x+y\right)\)
c: \(=10x\left(x-y\right)+8\left(x-y\right)=2\left(x-y\right)\left(5x+4\right)\)
d: \(=\left(x+y\right)^3-\left(x+y\right)\)
=(x+y)(x+y+1)(x+y-1)
e: =x^2+8x-x-8
=(x+8)(x-1)
f: \(=2x^2-4x+x-2=\left(x-2\right)\left(2x+1\right)\)
g: =-5x^2+15x+x-3
=(x-3)(-5x+1)
h: =x^2-3xy+xy-3y^2
=x(x-3y)+y(x-3y)
=(x-3y)*(x+y)
Bài 4:
a: \(=7xy\left(2-3-4\right)=-35xy\)
b: \(=\left(x-5\right)\left(x+y\right)\)
c: \(=10x\left(x-y\right)+8\left(x-y\right)=2\left(x-y\right)\left(5x+4\right)\)
d: \(=\left(x+y\right)^3-\left(x+y\right)\)
=(x+y)(x+y+1)(x+y-1)
e: =x^2+8x-x-8
=(x+8)(x-1)
f: \(=2x^2-4x+x-2=\left(x-2\right)\left(2x+1\right)\)
g: =-5x^2+15x+x-3
=(x-3)(-5x+1)
h: =x^2-3xy+xy-3y^2
=x(x-3y)+y(x-3y)
=(x-3y)*(x+y)
\(x^2-25-\left(x-5\right)=0\)
\(\Leftrightarrow\left(x^2-25\right)-\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+5\right)-\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+5-1\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+4\right)=0\)
+)TH1: \(x-5=0\Leftrightarrow x=5\)
+)TH2: \(x+4=0\Leftrightarrow x=-4\)
Vậy x-5 hoặc x=-4
\(x^2-25-\left(x-5\right)=0\)
⇔ \(x^2\) -25 -x + 5 = 0
⇔ x\(^2\) -x - 20 = 0
⇔ \(x^2+4x-5x-20=0\)
⇔ \(\left(x^2-5x\right)+\left(4x-20\right)=0\)
⇔ x( x - 5 ) + 4( x - 5 ) = 0
⇔ ( x - 5 ) ( x+ 4 ) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-4\end{matrix}\right.\)
\(x^2\left(x^2+5\right)-4x^2-20=0\)
⇔ \(x^4+5x^2-4x^2-20=0\)
⇔\(x^4+x^2-20=0\)
thay x\(^2\) bằng t ( t ≥ 0 ) ta có:
pt⇔ \(t^2+t-20=0\)
⇔ \(t^2+5t-4t-20=0\)
⇔ \(\left(t-4\right)\left(t+5\right)\)
⇔\(\left[{}\begin{matrix}t-4=0\\t+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}t=4\left(tm\right)\\t=-5\left(ktm\right)\end{matrix}\right.\)
* \(t=4\) ⇔ \(x^2=4\) ⇔ x = \(\pm2\)
\( {x^2}\left( {{x^2} + 5} \right) - 4{x^2} - 20 = 0\\ \Leftrightarrow {x^4} + 5{x^2} - 4{x^2} - 20 = 0\\ \Leftrightarrow {x^4} + {x^2} - 20 = 0 \)
Đặt \(x^2=t(t\ge0)\)
PT trở thành: \(t^2+t-20=0\)
\(\Leftrightarrow t=4\)(thỏa điều kiện); \(t=-5\)(không thỏa điều kiện)
Với \(t=4 \Rightarrow x^2=4 \Rightarrow x = \pm2\)
Vậy \(S=\left\{2;-2\right\}\)