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\(x^2-9=\left(x-3\right)\left(x+3\right)\)
\(\left(\dfrac{21+\left(x-4\right)\left(x+3\right)-\left(x-1\right)\left(x-3\right)}{x^2-9}\right):\left(1-\dfrac{1}{x+3}\right)=\left(\dfrac{3\left(x+2\right)}{x^2-9}\right):\left(\dfrac{x+2}{x+3}\right)=\left(x-3\right)\)
c/ \(C'=\frac{1}{\frac{1}{3-2\sqrt{x}}}.\frac{1}{\frac{1}{\sqrt{3-2\sqrt{x}}}+1}=\frac{\sqrt{\left(3-2\sqrt{x}\right)^3}}{1+\sqrt{\left(3-2\sqrt{x}\right)}}\)
Đặt \(\sqrt{\left(3-2\sqrt{x}\right)}=a\)
\(\Rightarrow C'=\frac{a^3}{a+1}=a^2-a+1-\frac{1}{a+1}\)
Đế C' nguyên thì a + 1 là ước của 1
\(\Rightarrow a=0\)
\(\Rightarrow\sqrt{\left(3-2\sqrt{x}\right)}=0\)
\(\Rightarrow x=\frac{9}{4}\left(l\right)\)
Vậy không có x.
Không biết có nhầm chỗ nào không nữa. Lam biếng kiểm tra lại quá. You kiểm tra lại hộ nhé. Thanks
a/ \(C=\left(\frac{2\sqrt{x}}{2x-5\sqrt{x}+3}-\frac{5}{2\sqrt{x}-3}\right):\left(3+\frac{2}{1-\sqrt{x}}\right)\)
\(=\left(\frac{2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(2\sqrt{x}-3\right)}-\frac{5}{2\sqrt{x}-3}\right):\left(\frac{3\sqrt{x}-5}{\sqrt{x}-1}\right)\)
\(=\left(\frac{2\sqrt{x}-5\sqrt{x}+5}{\left(\sqrt{x}-1\right)\left(2\sqrt{x}-3\right)}\right):\left(\frac{3\sqrt{x}-5}{\sqrt{x}-1}\right)\)
\(=\frac{5-3\sqrt{x}}{\left(\sqrt{x}-1\right)\left(2\sqrt{x}-3\right)}.\frac{\sqrt{x}-1}{3\sqrt{x}-5}\)
\(=\frac{1}{3-2\sqrt{x}}\)
Câu b, c tự làm nhé
Mình làm cho bạn 2 câu khó hơn còn mấy câu còn lại dungf phương pháp quy đồng rồi chuyển vế là tính được mà
c, <=> [(x-1)/2009 ]-1 +[ (x-2)/2008] -1 = [(x-3)/2007]-1 +[(x-4)/2006]-1
<=> (x-2010)/2009 + (x-2010)/2008 = (x-2010)/2007 + (x-2010)/2006
<=> (x-2010)*(1/2009+1/2008-1/2007-1/2006)=0
=> x-2010=0 => x=2010
d, TH1 : cả hai cùng âm
=>> 2X-4 <O => X< 2
Và 9-3x<0 =>> x> 3
=>> loại
Th2 cả hai cùng dương
2x-4>O => x>2
Và 9-3x>O => x<3
=>> 2<x<3 (tm)
\(M=\left(\frac{1+x}{1-x}-\frac{1-x}{1+x}-\frac{4x^2}{x^2-1}\right):\frac{4\left(x^2-3\right)}{x\left(1-x\right)}\)
\(=\left(\frac{1+x}{1-x}-\frac{1-x}{1+x}+\frac{4x^2}{1-x^2}\right).\frac{x\left(1-x\right)}{4\left(x^3-3\right)}\)
\(=\left(\frac{\left(1+x\right)^2}{\left(1-x\right)\left(1+x\right)}-\frac{\left(1-x\right)^2}{\left(1+x\right)\left(1-x\right)}+\frac{4x^2}{\left(1+x\right)\left(1-x\right)}\right).\frac{x\left(1-x\right)}{4\left(x^3-3\right)}\)
\(=\left(\frac{\left(1+x\right)^2-\left(1-x\right)^2+4x^2}{\left(1-x\right)\left(1+x\right)}\right).\frac{x\left(1-x\right)}{4\left(x^3-3\right)}\)
\(=\frac{\left(1+x+1-x\right)\left(1+x-1+x\right)+4x^2}{\left(1-x\right)\left(1+x\right)}.\frac{x\left(1-x\right)}{4\left(x^3-3\right)}\)
\(=\frac{2.2x+4x^2}{\left(1+x\right)}.\frac{x}{4\left(x^3-3\right)}\)
\(=\frac{4x+4x^2}{\left(1+x\right)}.\frac{x}{4\left(x^3-3\right)}\)
\(=\frac{4x\left(1+x\right)}{\left(1+x\right)}.\frac{x}{4\left(x^3-3\right)}\)
\(=\frac{x}{1}.\frac{x}{\left(x^3-3\right)}\)
\(=\frac{x^2}{x^3-3}\)
a)\(\left(0,25^{10}\right).4^{10}.\sqrt{5^2-3^2}=\left(0,25.4\right)^{10}.\sqrt{25-9}=1^{10}.\sqrt{16}=1.4=4\)
b)\(\frac{\left(-3\right)^6.15^5+9^3.\left(-15\right)^6}{\left(-3\right)^{10}.5^5.2^3}=\frac{3^6.15^5+3^6.15^6}{3^{10}.5^5.2^3}=\frac{3^6.15^5.\left(1+15\right)}{3^{10}.5^5.2^3}\)\(=\frac{3^{11}.5^5.16}{3^{10}.5^5.2^3}=3.2=6\)
2)a)\(4-\left|x+\frac{2}{3}\right|=-1\Rightarrow\left|x+\frac{2}{3}\right|=5\Rightarrow\orbr{\begin{cases}x+\frac{2}{3}=5\\x+\frac{2}{3}=-5\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{13}{3}\\x=\frac{-17}{3}\end{cases}}\)
b)\(\frac{x-2}{-9}=\frac{16}{2-x}\Rightarrow\left(x-2\right)^2=144\Rightarrow\orbr{\begin{cases}x-2=12\\x-2=-12\end{cases}\Rightarrow\orbr{\begin{cases}x=14\\x=-10\end{cases}}}\)
c)\(\frac{2}{3}x+\frac{1}{7}=\frac{5}{3}\Rightarrow\frac{2}{3}x=\frac{32}{21}\Rightarrow x=\frac{16}{7}\)
câu 2
\(...=\sqrt{\left(2-\sqrt{5}\right)^2}-\sqrt{\left(2+\sqrt{5}\right)^2}=\left|2-\sqrt{5}\right|-\left|2+\sqrt{5}\right|=-4\)
câu 1
\(P=\left(\frac{\sqrt{x}}{3+\sqrt{x}}+\frac{x+9}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right):\left(\frac{3\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-3\right)}-\frac{1}{\sqrt{x}}\right)\)
\(=\left(\frac{\sqrt{x}\left(3-\sqrt{x}\right)+x+9}{\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)}\right):\left(\frac{3\sqrt{x}+1-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\frac{3\sqrt{x}+9}{\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)}:\frac{2\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(=\frac{3}{\left(3-\sqrt{x}\right)}.\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\sqrt{x}+4}=\frac{-3\sqrt{x}}{2\sqrt{x}+4}\)
\(P< -1\Leftrightarrow\frac{-3\sqrt{x}}{2\sqrt{x}+4}+1< 0\Leftrightarrow-\sqrt{x}+4< 0\Leftrightarrow\sqrt{x}>4\Leftrightarrow x>16\)
a) \(\left(x-\frac{2}{5}\right).\left(x+\frac{3}{7}\right)0\) \(x+\frac{3}{7}-\frac{3}{7}\) \(x
dễ mà bn