\(\sqrt{\frac{x^2+2}{x^2-1}}-\sqrt{\frac{x^2+3}{x^2+1}}=1\)...">
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31 tháng 3 2020

a, Ta có : \(\frac{x+1}{2}+\frac{x-2}{4}=1-\frac{2\left(x-1\right)}{3}\)

=> \(\frac{6\left(x+1\right)}{12}+\frac{3\left(x-2\right)}{12}=\frac{12}{12}-\frac{8\left(x-1\right)}{12}\)

=> \(6\left(x+1\right)+3\left(x-2\right)=12-8\left(x-1\right)\)

=> \(6x+6+3x-6=12-8x+8\)

=> \(17x=20\)

=> \(x=\frac{20}{17}\)

b, Ta có : \(\frac{5x-1}{6}+x=\frac{6-x}{4}\)

=> \(\frac{5x-1+6x}{6}=\frac{6-x}{4}\)

=> \(4\left(11x-1\right)=6\left(6-x\right)\)

=> \(44x-4-36+6x=0\)

=> \(\)\(50x=40\)

=> \(x=\frac{4}{5}\)

c, Ta có : \(\frac{5\left(1-2x\right)}{3}+\frac{x}{2}=\frac{3\left(x-5\right)}{4}-2\)

=> \(\frac{20\left(1-2x\right)}{12}+\frac{6x}{12}=\frac{9\left(x-5\right)}{12}-\frac{24}{12}\)

=> \(20\left(1-2x\right)+6x=9\left(x-5\right)-24\)

=> \(20-40x+6x-9x+45+24=0\)

=> \(43x=89\)

=> \(x=\frac{89}{43}\)

20 tháng 6 2019

\(\sqrt{x-2\sqrt{x-3}-2}=1\)

=> \(x-2\sqrt{x-3}=1^2=1\)

=> \(-2\sqrt{x-3}=1-x+2\)

=> \(-2\sqrt{x-3}=3-x\)

=> \(\left(-2\sqrt{x-3}\right)^2=\left(3-x\right)^2\)

=> \(4\left(x-3\right)=9-6x+x^2\)

=> \(4x-12=9-6x+x^2\)

=> \(4x-12-9+6x-x^2=0\)

=> \(10x-21-x^2=0\)

Mình xin hết ( biết có vậy )

20 tháng 6 2019

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

\(\Leftrightarrow\sqrt{x-3-2\sqrt{x-3}+1}=1\)

\(\Leftrightarrow\sqrt{\left(\sqrt{x-3}-1\right)^2}=1\)

\(\Leftrightarrow\left|\sqrt{x-3}-1\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}-1=1\\\sqrt{x-3}-1=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=3\end{matrix}\right.\)

Vậy....

9 tháng 4 2020

a)

\(\frac{7}{x-5}-2=\frac{3}{5-x}\\ \Leftrightarrow\frac{-7}{5-x}-2-\frac{3}{5-x}=0\\ \Leftrightarrow\frac{-7}{5-x}-\frac{10-2x}{5-x}-\frac{3}{5-x}=0\\ \Leftrightarrow\frac{-7-10+2x-3}{5-x}=0\\ \Leftrightarrow\frac{2x-20}{5-x}=0\\ \Rightarrow2x-20=0\\ \Rightarrow x=10\)

b)

\(\frac{2}{x+1}-\frac{1}{x-2}=\frac{3x-11}{\left(x+1\right)\cdot\left(x-2\right)}\\ \Leftrightarrow\frac{2}{x+1}-\frac{1}{x-2}-\frac{3x-11}{\left(x+1\right)\cdot\left(x-2\right)}=0\\ \Leftrightarrow\frac{2x-4}{\left(x+1\right)\cdot\left(x-2\right)}-\frac{x+1}{\left(x+1\right)\cdot\left(x-2\right)}-\frac{3x-11}{\left(x+1\right)\cdot\left(x-2\right)}=0\\ \Leftrightarrow\frac{2x-4-x-1-3x+11}{\left(x+1\right)\cdot\left(x-2\right)}=0\\ \Leftrightarrow\frac{6-2x}{\left(x+1\right)\cdot\left(x-2\right)}=0\\ \Rightarrow6-2x=0\\ \Rightarrow x=3\)

c)

\(\frac{1}{x}-\frac{x+2}{x-2}=\frac{2}{x\cdot\left(2-x\right)}\\ \Leftrightarrow\frac{1}{x}-\frac{x-2}{2-x}-\frac{2}{x\cdot\left(2-x\right)}=0\\ \Leftrightarrow\frac{2-x}{x\cdot\left(2-x\right)}-\frac{x^2-2x}{x\cdot\left(2-x\right)}-\frac{2}{x\cdot\left(2-x\right)}=0\\ \Leftrightarrow\frac{2-x-x^2+2x-2}{x\cdot\left(2-x\right)}=0\\ \Leftrightarrow\frac{x-x^2}{x\cdot\left(2-x\right)}=0\\ \Rightarrow x-x^2=0\\ \Rightarrow x\cdot\left(1-x\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

Y
5 tháng 6 2019

Đặt \(x-3=t\) thì pt đã cho trở thành :

\(\frac{3}{t}-\frac{2}{t+2}=\frac{t+2}{2}-\frac{t}{3}\)

\(\Leftrightarrow\frac{3t+6-2t}{t\left(t+2\right)}=\frac{3t+6-2t}{6}\)

\(\Leftrightarrow\left(t+6\right)\left[\frac{1}{t\left(t+2\right)}-\frac{1}{6}\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}t+6=0\\\frac{1}{t\left(t+2\right)}=\frac{1}{6}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}t=-6\\t^2+2t-6=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=-6\\\left(t+1\right)^2=7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\t=\sqrt{7}-1\\t=-\sqrt{7}-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=2+\sqrt{7}\\x=2-\sqrt{7}\end{matrix}\right.\) ( TM )

NV
22 tháng 6 2019

\(x=\frac{1}{2}\frac{\sqrt{\left(\sqrt{2}-1\right)^2}}{\sqrt{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}}=\frac{1}{2}.\left(\sqrt{2}-1\right)\)

\(\Rightarrow2x=\sqrt{2}-1\Rightarrow2x+1=\sqrt{2}\)

\(\Rightarrow4x^2+4x+1=2\Rightarrow4x^2+4x-1=0\)

\(B=\left[x^3\left(4x^2+4x-1\right)-x\left(4x^2+4x-1\right)+4x^2+4x-1-1\right]^{2018}+2018\)

\(=\left(-1\right)^{2018}+2018=2019\)

15 tháng 12 2019

\(ĐK:x\ne\pm1\)

\(PT\Leftrightarrow\frac{3x+2}{\left(x-1\right)^2}-\frac{6}{\left(x+1\right)\left(x-1\right)}-\frac{3x-2}{\left(x+1\right)^2}\)

Bạn tự quy đồng rồi rút gọn nhé!!

\(=\dfrac{x^5\left(x^2+x+1\right)+x^2\left(x^2+x+1\right)+\left(x+1\right)}{x^2-1}\)

\(=\dfrac{x^2\left(x^2+x+1\right)\left(x+1\right)\left(x^2-x+1\right)+\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}\)

\(=\dfrac{x^2\left(x^2+x+1\right)\left(x^2-x+1\right)+1}{x-1}\)

 

6 tháng 2 2019

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6 tháng 2 2019

thanh niên thiếu hết đkxđ :v

(4x2)(10x+4)(5x+7)(2x+1)+17=0(4x−2)(10x+4)(5x+7)(2x+1)+17=0

(4x2)(5x+7)(10x+4)(2x+1)+17=0⇔(4x−2)(5x+7)(10x+4)(2x+1)+17=0

(20x2+18x14)(20x2+18x+4)+17=0⇔(20x2+18x−14)(20x2+18x+4)+17=0

Đặt t= 20x2+18x+4(t0)20x2+18x+4(t≥0) ta có:

(t-18).t +17=0

t218t+17=0⇔t2−18t+17=0

(t17)(t1)=0⇔(t−17)(t−1)=0

[t=17(tm)t=1(tm)⇔[t=17(tm)t=1(tm) [20x2+18x+4=1720x2+18x+4=1[20x2+18x13=020x2+18+3=0⇔[20x2+18x+4=1720x2+18x+4=1⇔[20x2+18x−13=020x2+18+3=0

[(20x+9341)(20x+9+341)=0(20x+921)(20x+9+21)=0⇔[(20x+9−341)(20x+9+341)=0(20x+9−21)(20x+9+21)=0

x=9+34120x=934120x=9+2120x=92120

6 tháng 6 2019

\(a,\)\(\left(4x-2\right)\left(10x+4\right)\left(5x+7\right)\left(2x+1\right)+17\)

\(=\left(4x-2\right)\left(5x+7\right)\left(10x+4\right)\left(2x+1\right)+17\)

\(=\left(20x^2+18x-5\right)\left(20x^2+18x+4\right)+17\)

Đặt ....