Violympic toán 9
Các câu hỏi tương tự
LARGE 7)Gfrac{sqrt{x}+1}{x-1}+frac{sqrt{x}-1}{sqrt{x}+1}-frac{2sqrt{x}+2}{x-1}Gfrac{sqrt{x}+1}{sqrt{x}-1}+frac{sqrt{x}-1}{sqrt{x}+1}-frac{2(sqrt{x}+1)}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{sqrt{x}+1}{x-1}+frac{sqrt{x}-1}{sqrt{x}+1}-frac{2}{sqrt{x}-1}Gfrac{(sqrt{x}+1)^2+(sqrt{x}-1)^2-2(sqrt{x}+1)}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{2x-2sqrt{x}}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{2sqrt{x}(sqrt{x}-1)}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{2sqrt{x}}{sqrt{x}+1}8)H(frac{1}{sqrt{x}-1}+frac{sqrt{x}}{x-1}):(frac{sqrt{x}}{sqrt{x}-1}-...
Đọc tiếp
\[\LARGE 7)G=\frac{\sqrt{x}+1}{x-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{2\sqrt{x}+2}{x-1}\\G=\frac{\sqrt{x}+1}{\sqrt{x}-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{2(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{\sqrt{x}+1}{x-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{2}{\sqrt{x}-1}\\G=\frac{(\sqrt{x}+1)^2+(\sqrt{x}-1)^2-2(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{2x-2\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{2\sqrt{x}(\sqrt{x}-1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{2\sqrt{x}}{\sqrt{x}+1}\\8)H=(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}):(\frac{\sqrt{x}}{\sqrt{x}-1}-1)\\H=(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}):(\frac{\sqrt{x}-(\sqrt{x}-1)}{\sqrt{x}-1})\\H=\frac{\sqrt{x}+1+\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}:\frac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}-1}\\H=\frac{2\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}:\frac{1}{\sqrt{x}-1}\\H=\frac{2\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}.(\sqrt{x}-1)\\H=\frac{2\sqrt{x}}{\sqrt{x}+1}\]
Giải phương trình:
\(a)\sqrt{x^2+2x+4}\ge x-2\\ b)x=\sqrt{x-\frac{1}{x}}+\sqrt{x+\frac{1}{x}}\\ c)\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2\sqrt{2x-5}}\\ d)x+y+z+4=2\sqrt{x-2}+4\sqrt{y-3}+6\sqrt{z-5}\\ e)\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\frac{1}{2}\left(x+y+z\right)\)
Giải HPT:
\(\left\{{}\begin{matrix}\frac{1}{\sqrt{x^2+1}}+\frac{1}{\sqrt{y^2+1}}=\frac{2}{\sqrt{xy+1}}\\x+\frac{y\sqrt{3}}{\sqrt{xy-3}}=2\sqrt{6}\end{matrix}\right.\)
Cho \(A=\left(2-\frac{2\sqrt{xy}+1}{\sqrt{xy}+1}+\frac{1}{1-\sqrt{xy}}+\frac{2\sqrt{x}}{1-xy}\right):\left(\frac{\sqrt{xy}-\sqrt{x}}{\sqrt{xy}+1}-\frac{\sqrt{xy+\sqrt{x}}}{\sqrt{xy}-1}\right)\)
a, Cho \(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}=12\) Chứng minh \(A\le36\) b, Cho \(x^2+9y^2=18\) . Tính GTNN của A
\(\left\{{}\begin{matrix}\frac{1}{\sqrt{x}}+\sqrt{2-\frac{1}{y}}=2\\\frac{1}{\sqrt{y}}+\sqrt{2-\frac{1}{x}}=2\end{matrix}\right.\)
Cho biểu thức A=\(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right):\left(3+\frac{1}{\sqrt{x}-2}+\frac{2}{\sqrt{x}+1}\right)\)
Rút gọn A?
b, Tính A biết x=\(\frac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}+\sqrt{83-18\sqrt{2}}\)
a. A(frac{3x+16sqrt{x}-7}{x+2sqrt{x}-3}-frac{sqrt{x}+1}{sqrt{x}+3}-frac{sqrt{x}+7}{sqrt{x}-1}) : (2-frac{sqrt{x}}{sqrt{x}-1})
b. B(frac{sqrt{x}+1}{sqrt{xy}+1}+frac{sqrt{xy}+sqrt{x}}{1-sqrt{xy}}+1) :( 1-frac{sqrt{xy}+sqrt{x}}{sqrt{xy}-1}-frac{sqrt{x}+1}{sqrt{xy}+1})
c. C( frac{sqrt{x}-4x}{1+4x}-1):(frac{1+2x}{1-4x}-frac{2sqrt{x}}{2sqrt{x}}-1)
d. D(frac{sqrt{a-b}}{sqrt{a+b}+sqrt{a+b}}+frac{a-b}{sqrt{a^2-b^2}-a+b})frac{a^2+b^2}{sqrt{a^2-b^2}}
e. Efrac{left(sqrt{a}-sqrt{b}right)+4sqrt{ab}}{sqrt{...
Đọc tiếp
a. A=(\(\frac{3x+16\sqrt{x}-7}{x+2\sqrt{x}-3}-\frac{\sqrt{x}+1}{\sqrt{x}+3}-\frac{\sqrt{x}+7}{\sqrt{x}-1}\)) : (\(2-\frac{\sqrt{x}}{\sqrt{x}-1}\))
b. B=(\(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\)) :( 1-\(\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\))
c. C=( \(\frac{\sqrt{x}-4x}{1+4x}-1\)):(\(\frac{1+2x}{1-4x}-\frac{2\sqrt{x}}{2\sqrt{x}}-1\))
d. D=(\(\frac{\sqrt{a-b}}{\sqrt{a+b}+\sqrt{a+b}}+\frac{a-b}{\sqrt{a^2-b^2}-a+b}\))\(\frac{a^2+b^2}{\sqrt{a^2-b^2}}\)
e. E=\(\frac{\left(\sqrt{a}-\sqrt{b}\right)+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\frac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}-b\)
Bài 1: Tính :
Csqrt{frac{3sqrt{3}-4}{2sqrt{3}+1}}-sqrt{frac{sqrt{3}+4}{5-2sqrt{3}}}
Bfrac{1}{sqrt{1}+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+frac{1}{sqrt{3}+sqrt{4}}+....+frac{1}{sqrt{99}+sqrt{100}}
Dsqrt{1+sqrt{3+sqrt{13+4sqrt{3}}}}+sqrt{1-sqrt{3-sqrt{13-4sqrt{3}}}}
Bài 2 : Cho Pleft(frac{1}{sqrt{x}-1}+frac{x-sqrt{x}+6}{x+sqrt{x}-2}right):left(frac{sqrt{x}+1}{sqrt{x}+2}+frac{x-sqrt{x}-2}{x+sqrt{x}+2}right)
a, Rút gọn P
b, Tìm GTNN
c, Tìm x để P.frac{x-1}{x^2+8x} -2
Đọc tiếp
Bài 1: Tính :
\(C=\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
\(B=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+....+\frac{1}{\sqrt{99}+\sqrt{100}}\)
\(D=\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Bài 2 : Cho \(P=\left(\frac{1}{\sqrt{x}-1}+\frac{x-\sqrt{x}+6}{x+\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}+2}+\frac{x-\sqrt{x}-2}{x+\sqrt{x}+2}\right)\)
a, Rút gọn P
b, Tìm GTNN
c, Tìm x để \(P.\frac{x-1}{x^2+8x}< -2\)
Xác định gt các bt sau:
\(a.A=\frac{xy-\sqrt{x^2-1}.\sqrt{y^2-1}}{xy+\sqrt{x^2-1}.\sqrt{y^2-1}}\) với \(x=\frac{1}{2}\left(a+\frac{1}{a}\right),y=\frac{1}{2}\left(b+\frac{1}{b}\right)\) (a>1; b>1)
\(b.B=\frac{\sqrt{a+bx}+\sqrt{a-bx}}{\sqrt{a+bx}-\sqrt{a-bx}}\) với \(x=\frac{2am}{b\left(1+m^2\right)},\left|m\right|< 1\)