\(\dfrac{1}{3\left(1+\sqrt{2}\right)}+\dfrac{1}{5\left(\sqrt{2}+\sqrt{3}\right)}+\dfrac{1}{7\left(\sqrt{3}+\sqrt{4}\right)}+...+\dfrac{1}{97\left(\sqrt{48}+\sqrt{49}\right)}< \dfrac{7}{3}\)
\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{36}\\\\\dfrac{4}{x}+\dfrac{3}{y}=\dfrac{1}{2}\\\end{matrix}\right.\)
chứng minh rằng:\(\dfrac{1}{3\left(\sqrt{1}+\sqrt{2}\right)}+\dfrac{1}{5\left(\sqrt{2}+\sqrt{3}\right)}+\dfrac{1}{7\left(\sqrt{3}+\sqrt{4}\right)}+...+\dfrac{1}{97\left(\sqrt{48}+\sqrt{49}\right)}< \dfrac{3}{7}\)
giải hệ pt
a)\(\left\{{}\begin{matrix}\dfrac{1}{x-2}+\dfrac{1}{2y-1}=2\\\dfrac{2}{x-2}-\dfrac{3}{2y-1}\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\dfrac{4}{x+y-1}-\dfrac{5}{7x-y+3}=\dfrac{5}{2}\\\dfrac{3}{x+y-1}+\dfrac{1}{2x-y+3}=\dfrac{7}{5}\end{matrix}\right.\)
\(\dfrac{4}{\left(2+\dfrac{2}{1+\dfrac{4}{5}}\right)x-\left(1+\dfrac{4}{2+\dfrac{1}{1+\dfrac{7}{8}}}\right)}+\dfrac{1}{\left(2+\dfrac{1}{3+\dfrac{1}{4}}\right)}=4+\dfrac{2}{1+\dfrac{8}{9}}\)
Tìm x biết: (viết kết quả dưới dạng hổn số)
\(\left(\dfrac{x+2\sqrt{x}-7}{x-9}+\dfrac{\sqrt{x}+1}{3-\sqrt{x}}\right):\left(\dfrac{1}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-1}\right)\)
\(\dfrac{\sqrt{a}+3}{\sqrt{a}-2}-\dfrac{\sqrt{a}-1}{\sqrt{a}+2}+\dfrac{4\sqrt{a}-4}{4-a}\)
RÚT GONJ
Tìm x
1) \(\sqrt{\dfrac{3x-1}{x+2}}=2\)
2)\(\sqrt{\dfrac{5x-7}{2x- 1}}=2\)
3)\(\dfrac{\sqrt{x}-2}{\sqrt{x}+1}=\dfrac{\sqrt{x}-1}{\sqrt{x}+3}\)
4) \(\dfrac{\sqrt{x}-3}{\sqrt{x}+2}=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\)
P=(\(\dfrac{x-2}{x+2\sqrt{x}}\)+\(\dfrac{1}{\sqrt{x+2}}\)).\(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\) với x >0 và x≠1
A=(\(\dfrac{2}{\sqrt{x}-2}\)+\(\dfrac{3}{2\sqrt{x+1}}\)-\(\dfrac{5\sqrt{x}-7}{2x-3\sqrt{x}-2}\)):\(\dfrac{2\sqrt{x}+3}{5x-10\sqrt{x}}\) với x > 0 và x≠4
A=\(\dfrac{x+1-2\sqrt{x}}{\sqrt{x-1}}\)+\(\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\) với x≥0 và x≠1
V=(\(\dfrac{1}{\sqrt{x}+2}\)+\(\dfrac{1}{\sqrt{x}-2}\))\(\dfrac{\sqrt{x}+2}{\sqrt{x}}\) với x>0 và x≠4
A=(\(\dfrac{1}{x-1}\)+\(\dfrac{3\sqrt{x}+5}{x\sqrt{x}-x-\sqrt{x}+1}\))(\(\dfrac{\left(\sqrt{x}+1\right)^2}{4\sqrt{x}}\)-1)
P=\(\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}\)+\(\dfrac{3\sqrt{x}-2}{1-\sqrt{x}}\)+\(\dfrac{2\sqrt{x}+3}{3+\sqrt{x}}\)
MỌI NGƯỜI GIÚP ĐỠ MÌNH RÚT GỌN MẤY BIỂU THỨC NÀY VỚI Ạ . EM XIN CẢM ƠN
giải các hệ phương trình
\(\left\{{}\begin{matrix}\dfrac{2x+1}{4}-\dfrac{y-2}{3}=\dfrac{1}{12}\\\dfrac{x+5}{2}=\dfrac{y+7}{3}-4\end{matrix}\right.\)
b2.
\(A=\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{5}}-\sqrt{2}\)
B3. Tìm ĐKXĐ
\(\dfrac{1}{x\sqrt{x}+1}-\dfrac{2}{\sqrt{x}+1}\)
b4. so sánh A với 1
A=\(\dfrac{\sqrt{x}}{x-\sqrt{x}+1}\)
b5.tính
a,\(\sin47+2\sin38-\cos43-\cos52\)
b, \(C=\dfrac{2\sin^2x-1}{\sin x-\cos x}\)