\(\sqrt{9x^2}=2x+1\)
<=> \(\sqrt{\left(3x\right)^2}=2x+1\)
<=> \(|3x|=2x+1\)
<=> \(\left[{}\begin{matrix}3x=-\left(2x+1\right)\\3x=2x+1\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}3x=-2x-1\\x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{5}\\x=1\end{matrix}\right.\)
CMR \(\dfrac{1}{a^3+1}+\dfrac{1}{b^3+1}+\dfrac{1}{c^3+1}\le\dfrac{1}{ab^2+1}+\dfrac{1}{bc^2+1}+\dfrac{1}{ca^2+1}\)
1.
A=\(\sqrt{1+\dfrac{1}{1^2}+\dfrac{1}{2^2}}+\sqrt{1+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+...+\sqrt{1+\dfrac{1}{99^2}+\dfrac{1}{100^2}}\)
\(P=\left(\dfrac{1-2a}{1+2a}1-\dfrac{1-4a+4a^2}{1+2a}\cdot\dfrac{1}{1-4a^2}\right)\cdot\left(\dfrac{1}{4a^2}+\dfrac{a+1}{a}\right)-\dfrac{1}{2a}\)
a) \(\dfrac{a-1}{\sqrt{b}-1}\).\(\sqrt{\dfrac{b-2\sqrt{b}+1}{\left(a-1\right).4}}\) (a,b≠1,b>0)
b) (1+\(\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\)).(1-\(\dfrac{a-\sqrt{a}}{\sqrt{a-1}}\)) (a≠1,a>0)
Tính giá trị B= \(\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+...+\sqrt{1+\frac{1}{99^2}+\frac{1}{100^2}}\)
Cho biểu thức \(A=\frac{\sqrt{1+x}}{\sqrt{1+x}-\sqrt{1-x}}+\frac{1-x}{\sqrt{1-x^2}-1+x}-\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\)
Tính A khi \(x=\frac{\sqrt{3}+1}{2\sqrt{2}}\)
1/√5-1 - 1/√5+1
giai phuong trinh 1/(2008x+1)-1/(2009x+2)=1/(2010x+4)-1/(1011x+5)
1) Tính giá trị biểu thức C=\(\sqrt{1+\dfrac{1}{1^2}+\dfrac{1}{2^2}}+\sqrt{1+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\sqrt{1+\dfrac{1}{3^2}+\dfrac{1}{4^2}}+...+\sqrt{1+\dfrac{1}{99^2}+\dfrac{1}{100^2}}\) 2) Chứng minh rằng với mọi số nguyên dương n ta đêu có \(\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+...+\sqrt{4}}}}}\) < 3 ( n căn bậc 4) Mọi người giúp em với ạ
