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ĐK: x khác 1; - 1
\(\frac{6}{x^2-1}+5=\frac{8x-1}{4x+4}-\frac{12x-1}{4-4x}.\)
<=> \(\frac{6}{x^2-1}+5=\frac{8x-1}{4x+4}+\frac{12x-1}{4x-4}.\)
<=> \(\frac{6.4}{4\left(x^2-1\right)}+\frac{5\left(x^2-1\right)}{4\left(x^2-1\right)}=\frac{\left(8x-1\right)\left(x-1\right)}{4\left(x^2-1\right)}+\frac{\left(12x-1\right)\left(x+1\right)}{4\left(x^2-1\right)}.\)
<=> \(24+20x^2-20=8x^2-x-8x+1+12x^2-x+12x-1\)
<=> \(2x=4\)
<=> x = 2 thỏa mãn.
1/
-x^3 -5x^2 + 4x +4
=> x1 =-5.5877............
x2=1.1895.............
x3=-0.6018............
a) \(x^4-4x^3+12x-9=0\)
\(\Leftrightarrow x^4-x^3-3x^3+3x^2-3x^2+3x+9x-9=0\)
\(\Leftrightarrow x^3\left(x-1\right)-3x^2\left(x-1\right)-3x\left(x-1\right)+9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-3x^2-3x+9\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x-3\right)-3\left(x-3\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-3\right)\left(x-3\right)=0\)
\(\Leftrightarrow x-1=0\)hoặc \(x^2-3=0\)hoặc \(x-3=0\)
\(\Leftrightarrow x=1\)hoặc \(x=\pm\sqrt{3}\)hoặc \(x=3\)
Vậy tập nghiệm của phương trình là : \(S=\left\{1;\pm\sqrt{3};3\right\}\)
b) \(x^5-5x^3+4x=0\)
\(\Leftrightarrow x^5-x^3-4x^3+4x=0\)
\(\Leftrightarrow x^3\left(x^2-1\right)-4x\left(x^2-1\right)=0\)
\(\Leftrightarrow\left(x^3-4x\right)\left(x^2-1\right)=0\)
\(\Leftrightarrow x\left(x^2-4\right)\left(x^2-1\right)=0\)
\(\Leftrightarrow x\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow x=0\)hoặc \(x=\pm2\)hoặc \(x=\pm1\)
Vậy tập nghiệm của phương trình là : \(S=\left\{0;\pm2;\pm1\right\}\)
c) \(x^4-4x^3+3x^2+4x-4=0\)
\(\Leftrightarrow x^4-x^3-3x^3+3x^2+4x-4=0\)
\(\Leftrightarrow x^3\left(x-1\right)-3x^2\left(x-1\right)+4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-3x^2+4=0\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-2x^2-x^2+4=0\right)\)
\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x-2\right)-\left(x-2\right)\left(x+2\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x^2+x+2\right)=0\)
\(\Leftrightarrow x-1=0\)
hoặc \(x^2+x+2=\left(x+\frac{1}{2}^2\right)+\frac{7}{4}=0\left(ktm\right)\)
hoặc \(x-2=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}\)
Vậy tập nghiệm của phương trình là \(S=\left\{1;2\right\}\)
\(\Leftrightarrow x^4-4x^3+12x^2-32x+32=\left(y-5\right)^2\)
\(\Leftrightarrow\left(x-2\right)^2\left(x^2+8\right)=\left(y-5\right)^2\)
- Với \(x=2\Rightarrow y=5\)
- Với \(x\ne2\Rightarrow x-2\) là ước của \(y-5\)
Đặt \(y-5=n\left(x-2\right)\)
\(\Rightarrow\left(x-2\right)^2\left(x^2+8\right)=n^2\left(x-2\right)^2\)
\(\Rightarrow x^2+8=n^2\)
\(\Rightarrow\left(n-x\right)\left(n+x\right)=8\)
\(\Rightarrow\left[{}\begin{matrix}x=1;n=-3\Rightarrow y=8\\x=-1;n=-3\Rightarrow y=14\\x=1;n=3\Rightarrow y=2\\x=-1;n=3\Rightarrow y=-4\end{matrix}\right.\)
1: \(\Leftrightarrow\left(x-4\right)^2+14=-9\left(x-4\right)\)
\(\Leftrightarrow x^2-8x+16+14+9x-36=0\)
\(\Leftrightarrow x^2+x-6=0\)
=>(x+3)(x-2)=0
=>x=-3(nhận) hoặc x=2(nhận)
2: \(\Leftrightarrow\left(8x+1\right)\left(2x-1\right)-2x\left(2x+1\right)-12x^2+9=0\)
\(\Leftrightarrow16x^2-8x+2x-1-4x^2-2x-12x^2+9=0\)
=>-8x+8=0
hay x=1(nhận)
c: \(\dfrac{1}{2\left(x-3\right)}-\dfrac{3x-5}{\left(x-3\right)\left(x-1\right)}=\dfrac{1}{2}\)
\(\Leftrightarrow x-1-2\left(3x-5\right)=\left(x-3\right)\left(x-1\right)\)
\(\Leftrightarrow x^2-4x+3=x-1-6x+10=-5x+9\)
\(\Leftrightarrow x^2+x-6=0\)
=>(x+3)(x-2)=0
=>x=-3(nhận) hoặc x=2(nhận)
\(ĐKXĐ:x\ne\pm1\)
\(\frac{6}{x^2-1}+5=\frac{8x-1}{4x+4}-\frac{12x-1}{4-4x}\)
\(\Leftrightarrow\frac{6}{\left(x-1\right)\left(x+1\right)}+5-\frac{8x-1}{4\left(x+1\right)}-\frac{12x-1}{4\left(x-1\right)}=0\)
\(\Leftrightarrow\frac{24+20\left(x^2-1\right)-\left(8x-1\right)\left(x-1\right)-\left(12x-1\right)\left(x+1\right)}{4\left(x-1\right)\left(x+1\right)}=0\)
\(\Leftrightarrow24+20x^2-20-8x^2+9x-1-12x^2-11x+1=0\)
\(\Leftrightarrow-2x+4=0\)
\(\Leftrightarrow x=2\)
Vậy tập nghiệm của phương trình là \(S=\left\{2\right\}\)
ĐKXĐ: \(x\ne\pm1\)
\(\frac{6}{x^2-1}+5=\frac{8x-1}{4x+4}-\frac{12x-1}{4-4x}\)
\(\Leftrightarrow\frac{6}{\left(x+1\right)\left(x-1\right)}+5=\frac{8x-1}{4\left(x+1\right)}-\frac{12x-1}{4\left(1-x\right)}\)
\(\Leftrightarrow24\left(1-x\right)+20\left(x+1\right)\left(x-1\right)\left(1-x\right)=\left(8x-1\right)\left(x-1\right)\left(1-x\right)\)\(-\left(12x-1\right)\left(x+1\right)\left(1-x\right)\)
\(\Leftrightarrow4-4x+20x^2-20x^3=18x^2-20x^3+2x\)
\(\Leftrightarrow4-4x+20x^2=18x^2+2x\)
\(\Leftrightarrow4-4x+20x^2-18x^2-2x=0\)
(x4-9)+(-4x3+12x)=0
(x2-3)(x2+3)-4x(x2+3)=0
(x2+3).(x2-4x-3)=0
mà x2+3 > 0 với mọi x nên x2-4x-3=0
bạn giải nốt nhé
mk là sai
(x2+3)(x2-3)-4x(x2-3)=0
(x2-3)(x2-4x+3)=0
\(x=\sqrt{3};-\sqrt{3};3;1\)
\(a,9\left(2x+1\right)=4\left(x-5\right)^2\)
\(4x^2-40x+100=18x+9\)
\(4x^2-58x+91=0\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{29+3\sqrt{53}}{4}\\x=\frac{29-3\sqrt{53}}{4}\end{cases}}\)
\(b,x^3-4x^2-12x+27=0\)
\(\left(x+3\right)\left(x^2-7x+9\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+3=0\\x^2-7x+9=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-3\\x=\frac{7\pm\sqrt{13}}{2}\end{cases}}}\)
\(c,x^3+3x^2-6x-8=0\)
\(\left(x+4\right)\left(x-2\right)\left(x+1\right)=0\)
\(Th1:x+4=0\Leftrightarrow x=-4\)
\(Th2:x-2=0\Leftrightarrow x=2\)
\(Th3:x+1=0\Leftrightarrow x=-1\)
\(a,9.\left(2x+1\right)=4.\left(x-5\right)^2\)
\(< =>4x^2-40x+100=18x+9\)
\(< =>4x^2+58x+91=0\)
\(< =>\orbr{\begin{cases}x=\frac{29-3\sqrt{53}}{4}\\x=\frac{29+3\sqrt{53}}{4}\end{cases}}\)
\(b,x^3-4x^2-12x+27=0\)
\(< =>\left(x+3\right)\left(x^2-7x+9\right)=0\)
\(< =>\orbr{\begin{cases}x+3=0\\x^2-7x+9=0\end{cases}}\)
\(< =>\orbr{\begin{cases}x=-3\\x=\frac{7\pm\sqrt{13}}{2}\end{cases}}\)
x^4 + 2x^3 + 5x^2 + 4x-12 = 0
<=> (x^4 - x^3) + (3x^3-3x^2) + (8x^2 - 8x) + (12x-12) = 0
<=> (x-1).(x^3 + 3x^2 + 8x+12) = 0
<=> (x-1).[(x^3+2x^2)+(x^2+2x)+(6x+12)] = 0
<=>(x-1).(x+2).(x^2+x+6) = 0
<=> x= 1 hoặc x = -2
x4 - 4x3 + 12x -9 = 0
<=> x4 - x3 - 3x3 + 3x2 - 3x2 + 3x + 9x - 9 = 0
<=> x3(x-1) - 3x2(x-1) - 3x(x-1) + 9(x-1) = 0
<=> (x-1)(x3 - 3x2 - 3x + 9) = 0
<=> (x-1)[x2(x-3) - 3(x-3)] = 0
<=> (x-1)(x-3)(x2 - 3) = 0
=> x-1 = 0 hoặc x - 3= 0 hoặc x2 - 3 = 0
=> x = 1 hoặc x = 3 hoặc x = \(\pm\sqrt{3}\)
Vậy S = ...
\(-x^5+4x^4=-12x^3\)
\(\Leftrightarrow x^5-4x^4-12x^3=0\)
\(\Leftrightarrow x^3\left(x^2-4x-12\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^2-4x-12=0\left(1\right)\end{cases}}\)
\(Pt\left(1\right)\Leftrightarrow\left(x+2\right)\left(x-6\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=-2\\x=6\end{cases}}\)
Vậy \(x\in\left\{-2;0;6\right\}\)
hok tốt