Cho \(f\left(x\right)\)=\(\frac{x+\sqrt{5}}{\sqrt{x}+\sqrt{x+\sqrt{5}}}\) + \(\frac{x-\sqrt{5}}{\sqrt{x}-\sqrt{x-\sqrt{5}}}\)
Tính f(3)?
Những câu hỏi liên quan
Cho \(f\left(x\right)=\frac{x+\sqrt{5}}{\sqrt{x}+\sqrt{x+\sqrt{5}}}+\frac{x-\sqrt{5}}{\sqrt{x}-\sqrt{x-\sqrt{5}}}\)
Tính \(f\left(3\right)\)
Cho \(f\left(x\right)=\dfrac{x+\sqrt{5}}{\sqrt{x}+\sqrt{x+\sqrt{5}}}+\dfrac{x-\sqrt{5}}{\sqrt{x}-\sqrt{x-\sqrt{5}}}\). Tính f(3)
\(\dfrac{x+\sqrt{5}}{\sqrt{x}+\sqrt{x+\sqrt{5}}}+\dfrac{x-\sqrt{5}}{\sqrt{x}-\sqrt{x-\sqrt{5}}}\)
\(=\dfrac{\left(x+\sqrt{5}\right)\cdot\left(\sqrt{x}-\sqrt{x+\sqrt{5}}\right)}{x-x-\sqrt{5}}+\dfrac{\left(x-\sqrt{5}\right)\left(\sqrt{x}+\sqrt{x-\sqrt{5}}\right)}{x-x+\sqrt{5}}\)
\(=\dfrac{\left(x+\sqrt{5}\right)\left(\sqrt{x}-\sqrt{x+\sqrt{5}}\right)+\left(-x+\sqrt{5}\right)\left(\sqrt{x}+\sqrt{x-\sqrt{5}}\right)}{\sqrt{5}}\)
\(=\dfrac{\left(3+\sqrt{5}\right)\left(\sqrt{3}-\sqrt{3+\sqrt{5}}\right)-\left(3-\sqrt{5}\right)\left(\sqrt{3}+\sqrt{3-\sqrt{5}}\right)}{\sqrt{5}}\)
\(=\dfrac{\left(6+2\sqrt{5}\right)\left(\sqrt{6}-\sqrt{6+2\sqrt{5}}\right)-\left(6-2\sqrt{5}\right)\left(\sqrt{6}+\sqrt{6-2\sqrt{5}}\right)}{\sqrt{5}}\)
\(=\dfrac{\left(6+2\sqrt{5}\right)\left(\sqrt{6}-\sqrt{5}-1\right)-\left(6-2\sqrt{5}\right)\left(\sqrt{6}+\sqrt{5}-1\right)}{\sqrt{5}}\)
\(=\dfrac{-12\sqrt{5}+4\sqrt{30}}{\sqrt{5}}\)
\(=-12+4\sqrt{6}\)
Đúng 2
Bình luận (1)
Cho \(f\left(x\right)=\dfrac{x+\sqrt{5}}{\sqrt{x}+\sqrt{x+\sqrt{5}}}+\dfrac{x-\sqrt{5}}{\sqrt{x}-\sqrt{x-\sqrt{5}}}\). Tính f(3)
Cho f(x)=\(\frac{x+\sqrt{5}}{\sqrt{x}+\sqrt{x+\sqrt{5}}}+\frac{x-\sqrt{5}}{\sqrt{x}-\sqrt{x-\sqrt{5}}}\). Tính f(3)
Cho f(x) =\(\frac{x+\sqrt{5}}{\sqrt{x}+\sqrt{x+\sqrt{5}}}\) +\(\frac{x-\sqrt{5}}{\sqrt{x}-\sqrt{x-\sqrt{5}}}\). Tính f(3)
Tính A=\(\left(\frac{2}{\sqrt{5}-3}-\frac{2}{\sqrt{5}+3}\right)×\frac{\sqrt{3}-3}{1-\sqrt{3}}+3\sqrt{27}\)
B=\(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)×\left(11+\sqrt{6}\right)\)
Tìm x để E=\(\sqrt{x-5}+\sqrt{7}\)nhỏ nhất
Tìm x để F=\(\frac{4-\sqrt{x}}{\sqrt{x}+2}\)lớn nhất
\(F=\left(\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{\sqrt{x}+1}{\sqrt{x}-2}-\frac{2\sqrt{x}+7}{x-4}\right):\left(\frac{3-\sqrt{x}}{\sqrt{x}-2}+1\right)\)
a,rút gọn
b,tính F biết x=9-\(4\sqrt{5}\)
c, tìm GTNN của F
1, \(f\left(x\right)\left\{{}\begin{matrix}\frac{x^2-2}{x-\sqrt{2}}\left(x\ne\sqrt{2}\right)\\2\sqrt{2}\left(x=\sqrt{2}\right)\end{matrix}\right.\)
2, \(f\left(x\right)=\left\{{}\begin{matrix}\frac{x-5}{\sqrt{2x-1}-3}\left(x>5\right)\\\left(x-5\right)^2+3\left(x\le5\right)\end{matrix}\right.\) tại x=5
a/ \(\lim\limits_{x\rightarrow\sqrt{2}}f\left(x\right)=\lim\limits_{x\rightarrow\sqrt{2}}\frac{\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)}{x-\sqrt{2}}=\lim\limits_{x\rightarrow\sqrt{2}}\left(x+\sqrt{2}\right)=2\sqrt{2}\)
\(\Rightarrow\lim\limits_{x\rightarrow\sqrt{2}}f\left(x\right)=f\left(\sqrt{2}\right)\Rightarrow\) hàm số liên tục tại \(x=\sqrt{2}\)
b/ \(\lim\limits_{x\rightarrow5^+}f\left(x\right)=\lim\limits_{x\rightarrow5^+}\frac{x-5}{\sqrt{2x-1}-3}=\frac{\left(x-5\right)\left(\sqrt{2x-1}+3\right)}{2\left(x-5\right)}=\lim\limits_{x\rightarrow5^+}\frac{\sqrt{2x-1}+3}{2}=3\)
\(f\left(5\right)=\lim\limits_{x\rightarrow5^-}f\left(x\right)=\lim\limits_{x\rightarrow5^-}\left[\left(x-5\right)^2+3\right]=5\)
\(\Rightarrow\lim\limits_{x\rightarrow5^+}f\left(x\right)=\lim\limits_{x\rightarrow5^-}f\left(x\right)=f\left(5\right)\Rightarrow\) hàm số liên tục tại \(x=5\)
Aleft(sqrt{5}-sqrt{2}right)^2-frac{9}{sqrt{10}-1}+sqrt{90}Bsqrt{2}left(3sqrt{2}+sqrt{3-sqrt{5}}right)-sqrt{5}Cleft(frac{5-sqrt{5}}{sqrt{5}-1}-frac{sqrt{5}+1}{5+sqrt{5}}right):frac{sqrt{5}+1}{sqrt{5}}Dfrac{xsqrt{y}-ysqrt{x}+sqrt{x}-sqrt{y}}{1+sqrt{xy}}:frac{x+2sqrt{xy}+y}{left(sqrt{x}+sqrt{y}right)^3left(x+yright)}vớix,y0TÍNH HOẶC RÚT GỌN
Đọc tiếp
\(A=\left(\sqrt{5}-\sqrt{2}\right)^2-\frac{9}{\sqrt{10}-1}+\sqrt{90}\)\(B=\sqrt{2}\left(3\sqrt{2}+\sqrt{3-\sqrt{5}}\right)-\sqrt{5}\)\(C=\left(\frac{5-\sqrt{5}}{\sqrt{5}-1}-\frac{\sqrt{5}+1}{5+\sqrt{5}}\right):\frac{\sqrt{5}+1}{\sqrt{5}}\)\(D=\frac{x\sqrt{y}-y\sqrt{x}+\sqrt{x}-\sqrt{y}}{1+\sqrt{xy}}:\frac{x+2\sqrt{xy}+y}{\left(\sqrt{x}+\sqrt{y}\right)^3\left(x+y\right)}vớix,y>0\)
TÍNH HOẶC RÚT GỌN