Violympic toán 9
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BL
25 tháng 4 2020 lúc 11:56
Gpt: a) sqrt[4]{3left(x+5right)}-sqrt[4]{11-x}sqrt[4]{13+x}-sqrt[4]{3left(3-xright)}
b) frac{1+2sqrt{x}-xsqrt{x}}{3-x-sqrt{2-x}}2left(frac{1+xsqrt{x}}{1+x}right) c) sqrt{x+1}+frac{4left(sqrt{x+1}+sqrt{x-2}right)}{3left(sqrt{x-2}+1right)^2}3
d) sqrt{frac{x-2}{x+1}}+frac{x+2}{left(sqrt{x+2}+sqrt{x-2}right)^2}1 e) 2x+1+xsqrt{x^2+2}+left(x+1right)sqrt{x^2+2x+2}0
f) sqrt{2x+3}cdotsqrt[3]{x+5}x^2+x-6
Đọc tiếp
Gpt: a) \(\sqrt[4]{3\left(x+5\right)}-\sqrt[4]{11-x}=\sqrt[4]{13+x}-\sqrt[4]{3\left(3-x\right)}\)
b) \(\frac{1+2\sqrt{x}-x\sqrt{x}}{3-x-\sqrt{2-x}}=2\left(\frac{1+x\sqrt{x}}{1+x}\right)\) c) \(\sqrt{x+1}+\frac{4\left(\sqrt{x+1}+\sqrt{x-2}\right)}{3\left(\sqrt{x-2}+1\right)^2}=3\)
d) \(\sqrt{\frac{x-2}{x+1}}+\frac{x+2}{\left(\sqrt{x+2}+\sqrt{x-2}\right)^2}=1\) e) \(2x+1+x\sqrt{x^2+2}+\left(x+1\right)\sqrt{x^2+2x+2}=0\)
f) \(\sqrt{2x+3}\cdot\sqrt[3]{x+5}=x^2+x-6\)
Tìm điều kiện x để các biểu thức sau \(a)\frac{x}{x^2-4}+\sqrt{x-2}\\ b)\frac{\sqrt{x}}{\left|x\right|-1}\\ c)\frac{2}{\left|x\right|+4}+\sqrt{x^2-4}\\ d)\frac{1}{\sqrt{x-2\sqrt{x-1}}}\\ e)\sqrt{x^2-2x}+3\sqrt{4-x^2}\)
Rút gọn A = \(1-\left(\frac{2x-1+\sqrt{x}}{1-x}+\frac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right).\left(\frac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\right)\)
Cho A=\(\left[\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{4x}{4-x}\right)-\frac{2-\sqrt{x}}{2+\sqrt{x}}\right]\div\frac{x-\sqrt{x}}{2\sqrt{x}-x}\)
a)Rút gọn A
b)Tìm A biết x=\(3+2\sqrt{2}\)
Cho P=1-\(\left[\frac{2x-1+\sqrt{x}}{1-\sqrt{x}}+\frac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right]\frac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\)
a, Rút gọn P
b, Tìm x thuộc Z để P thuộc Z
1.Chmr rằng nếu: a,b >0 thì \(\sqrt{a}+\sqrt{b}\le\sqrt{\frac{a^2}{b}}+\sqrt{\frac{b^2}{a}}\)
2. Rg biểu thức:
\(A=\frac{\sqrt{x-\sqrt{4\left(x-1\right)}}+\sqrt{x+\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(1-\frac{1}{x-1}\right)\)
Cho biểu thức Pleft(frac{2sqrt{x}}{sqrt{x}+3}+frac{sqrt{x}}{sqrt{x}-3}-frac{3x+3}{x-9}right):left(frac{2sqrt{x}-2}{sqrt{x}-3}-1right)
a)Rút gọn P
b)Tìm x để P frac{1}{2}
c)Tìm x để P.left(sqrt{x}+3right)+2sqrt{x}-2+x2
d)Tìm m để P.left(sqrt{x}+3right)+xleft(sqrt{x}-mright)x-sqrt{x}left(3+mright)
Đọc tiếp
Cho biểu thức \(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
a)Rút gọn P
b)Tìm x để \(P< \frac{1}{2}\)
c)Tìm x để \(P.\left(\sqrt{x}+3\right)+2\sqrt{x}-2+x=2\)
d)Tìm m để \(P.\left(\sqrt{x}+3\right)+x\left(\sqrt{x}-m\right)=x-\sqrt{x}\left(3+m\right)\)
Rút gọn A = \(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right) :\left(3+\frac{1}{\sqrt{x}-2}+\frac{2}{\sqrt{x}+1}\right)\)
a, Rút gọn A b , Tìm x thỏa mãn A > 1 c,Tính A với \(x=\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\)\(A=\frac{\sqrt{x}+1}{3\left(\sqrt{x}-1\right)}\)
1. Rút gọn
P=\(2\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}:\left[\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}-\frac{1}{2}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2\right]\)