giải phương trình:
a, (x - 2)4 + (x - 4)4 = 82
b, (x2 - 4x)2 + 2(x - 2)2 = 43
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TH
1
H9
HT.Phong (9A5)
CTVHS
24 tháng 10 2023
\(4x^2-5x-4\sqrt{x-1}-2=0\left(x\ge1\right)\)
\(\Leftrightarrow\left(4x^2-4x+1\right)-\left(x-1+4\sqrt{x-1}+4\right)=0\)
\(\Leftrightarrow\left(2x-1\right)^2-\left(\sqrt{x-1}+2\right)^2=0\)
\(\Leftrightarrow\left(2x-1-\sqrt{x-1}-2\right)\left(2x-1+\sqrt{x-1}+2\right)=0\)
\(\Leftrightarrow\left(2x-\sqrt{x-1}-3\right)\left(2x+\sqrt{x-1}+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-1}=2x-3\\\sqrt{x-1}=-\left(2x+1\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x\in\varnothing\end{matrix}\right.\)
Vậy với x = 2 thì thỏa mãn pt
13 tháng 2 2020
câu a bài 1:(2x+1)(3x-2)=(5x-8)(2x+1)
<=>(2x+1)(3x-2)-(5x-8)(2x+1)=0
<=>(2x+1)(3x-2-5x+8)=0
<=>(2x+1)(6-2x)=0
bước sau tự làm nốt nha !
câu b:gợi ý: tách 4x^2-1thành (2x-1)(2x+1) rồi làm như câu a
13 tháng 2 2020
Đặng Thị Vân Anh tuy mk k cần nx nhưng dù s cx cảm ơn bn nha :)
NN
0
1 tháng 1 2018
\(\text{a) }\left(x^2+x\right)^2+4\left(x^2+x\right)=12\\ \Leftrightarrow\text{Đặt }x^2+x=y\\ \Leftrightarrow y^2+4y=12\\ \Leftrightarrow y^2+6y-2y-12=0\\ \Leftrightarrow\left(y^2+6y\right)-\left(2y+12\right)=0\\ \Leftrightarrow y\left(y+6\right)-2\left(y+6\right)=0\\ \Leftrightarrow\left(y+6\right)\left(y-2\right)=0\\ \Leftrightarrow\left(x^2+x+6\right)\left(x^2+x-2\right)=0\\ \Leftrightarrow\left(x^2+x+\dfrac{1}{4}+\dfrac{23}{4}\right)\left(x^2+2x-x-2\right)=0\\ \Leftrightarrow\left[\left(x^2+x+\dfrac{1}{4}\right)+\dfrac{23}{4}\right]\left[\left(x^2+2x\right)-\left(x+2\right)\right]=0\\ \Leftrightarrow\left[\left(x+\dfrac{1}{2}\right)^2+\dfrac{23}{4}\right]\left[x\left(x+2\right)-\left(x+2\right)\right]=0\\ \Leftrightarrow\left(x-1\right)\left(x+2\right)=0\left(Vì\text{ }\left(x+\dfrac{1}{2}\right)^2+\dfrac{23}{4}\ne0\right)\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\\ \text{Vậy }S=\left\{1;-2\right\}\\ \)
\(\text{b) }6x^4-5x^3-38x^2-5x+6=0\\ \Leftrightarrow x^2\left(6x^2-5x-38-\dfrac{5}{x}+\dfrac{6}{x^2}\right)=0\\ \Leftrightarrow x^2\left[\left(6x^2+12+\dfrac{6}{x^2}\right)-\left(5x+\dfrac{5}{x}\right)-50\right]=0\\ \Leftrightarrow x^2\left[6\left(x^2+2+\dfrac{1}{x^2}\right)-5\left(x+\dfrac{1}{x}\right)-50\right]=0\\ \Leftrightarrow x^2\left[6\left(x+\dfrac{1}{x}\right)^2-5\left(x+\dfrac{1}{x}\right)-50\right]=0\\ \text{Đặt }x+\dfrac{1}{x}=y\\ \Leftrightarrow x^2\left(6y^2-5y-50\right)=0\\ \Leftrightarrow x^2\left(6y^2-20y+15y-50\right)=0\\ \Leftrightarrow x^2\left[\left(6y^2-20y\right)+\left(15y-50\right)\right]=0\\ \Leftrightarrow x^2\left[2y\left(3y-10\right)+5\left(3y-10\right)\right]=0\\ \Leftrightarrow x^2\left(2y+5\right)\left(3y-10\right)=0\\ \Leftrightarrow x^2\left(2x+\dfrac{2}{x}+5\right)\left(3x+\dfrac{3}{x}-10\right)=0\\ \Leftrightarrow\left(2x^2+2+5x\right)\left(3x^2+3-10x\right)=0\\ \Leftrightarrow\left(2x^2+4x+x+2\right)\left(3x^2-9x-x+3\right)=0\\ \Leftrightarrow\left[\left(2x^2+4x\right)+\left(x+2\right)\right]\left[\left(3x^2-9x\right)-\left(x-3\right)\right]=0\\ \Leftrightarrow\left[2x\left(x+2\right)+\left(x+2\right)\right]\left[3x\left(x-3\right)-\left(x-3\right)\right]=0\\ \Leftrightarrow\left(2x+1\right)\left(x+2\right)\left(3x-1\right)\left(x-3\right)=0\\ \)
\(\Leftrightarrow\left[{}\begin{matrix}2x+1=0\\x+2=0\\3x-1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=-1\\x=-2\\3x=1\\x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=-2\\x=\dfrac{1}{3}\\x=3\end{matrix}\right.\\ \text{Vậy }S=\left\{-\dfrac{1}{2};-2;\dfrac{1}{3};3\right\}\)
NH
1
NV
Nguyễn Việt Lâm
Giáo viên
29 tháng 6 2019
ĐKXĐ: ...
\(4x^2+\frac{1}{x^2}-4\left(2x+\frac{1}{x}\right)+7=0\)
Đặt \(2x+\frac{1}{x}=a\Rightarrow a^2=4x^2+\frac{1}{x^2}+4\Rightarrow4x^2+\frac{1}{x^2}=a^2-4\)
\(a^2-4-4a+7=0\)
\(\Leftrightarrow a^2-4a+3=0\Rightarrow\left[{}\begin{matrix}a=1\\a=3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x+\frac{1}{x}=1\\2x+\frac{1}{x}=3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}2x^2-x+1=0\\2x^2-3x+1=0\end{matrix}\right.\)
NV
Nguyễn Việt Lâm
Giáo viên
30 tháng 6 2019
\(\frac{2}{x^2+1}+\frac{4}{x^2+3}+\frac{6}{x^2+5}=3+\frac{x^2-1}{x^2+6}\)
\(\Leftrightarrow\frac{x^2-1}{x^2+6}+1-\frac{2}{x^2+1}+1-\frac{4}{x^2+3}+1-\frac{6}{x^2+5}=0\)
\(\Leftrightarrow\frac{x^2-1}{x^2+6}+\frac{x^2-1}{x^2+1}+\frac{x^2-1}{x^2+3}+\frac{x^2-1}{x^2+5}=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(\frac{1}{x^2+6}+\frac{1}{x^2+1}+\frac{1}{x^2+3}+\frac{1}{x^2+5}\right)=0\)
\(\Rightarrow x=\pm1\)
a/ Đặt \(x-3=t\)
\(\left(t+1\right)^4+\left(t-1\right)^4-82=0\)
\(\Leftrightarrow2t^4+12t^2-80=0\)
\(\Leftrightarrow t^4+6t^2-40=0\Rightarrow\left[{}\begin{matrix}t^2=4\\t^2=-10\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}t=2\\t=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=5\\x=1\end{matrix}\right.\)
b/ \(\Leftrightarrow\left(x^2-4x\right)^2+2\left(x^2-4x+4\right)-43=0\)
Đặt \(x^2-4x=t\)
\(t^2+2\left(t+4\right)-43=0\)
\(\Leftrightarrow t^2+2t-35=0\Rightarrow\left[{}\begin{matrix}t=5\\t=-7\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2-4x-5=0\\x^2-4x+7=0\left(vn\right)\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-1\\x=5\end{matrix}\right.\)