Violympic toán 9
Các câu hỏi tương tự
1. Rút gọn
P=\(2\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}:\left[\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}-\frac{1}{2}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2\right]\)
\(\frac{2\left(x+4\right)}{\left(\sqrt{x}+1\right)\left(x-4\right)}\)+\(\frac{\sqrt{x}}{\sqrt{x}+1}\)+\(\frac{8}{4-\sqrt{x}}\)
a, tìm đkxđ rút gọn
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) \(\sqrt{2x+3}\cdot\sqrt[3]{x+5}=x^2+x-6\)
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:
\(A=\frac{\sqrt{x-\sqrt{4\left(x-1\right)}}+\sqrt{x+\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(1-\frac{1}{x-1}\right)\)
a. sqrt{1-2x}x+7
b.sqrt{1+x^2}2x-1
c.sqrt{1-x}-sqrt{2+x}1
d. sqrt{1-x}+sqrt{4+x}3
e. left|2x+5right| x-1
f. left|xright|+left|2x-1right|x+2
g.left|x-9right|^{10}+left|x-10right|^{10}1
h. left|x-2014right|^{2015}+left|x-2015right|^{2014}1
i. sqrt{x+3+4sqrt{x-1}}+sqrt{x+8-6sqrt{x-1}}5
k. sqrt{x+2sqrt{x-1}}+sqrt{x-2sqrt{x-1}}x-1
l. sqrt{x+2-4sqrt{x-2}}+sqrt{x+7-6sqrt{x-2}}1
m. sqrt{x+8+2sqrt{x+7}}+sqrt{x-1-2sqrt{x+7}}4
m. x+sqrt{x+frac{1}{4}+sqrt{x+frac{1}{4}}}frac{9}{4}
n.left(x+5righ...
Đọc tiếp
a. \(\sqrt{1-2x}=x+7\)
b.\(\sqrt{1+x^2}=2x-1\)
c.\(\sqrt{1-x}-\sqrt{2+x}=1\)
d. \(\sqrt{1-x}+\sqrt{4+x}=3\)
e. \(\left|2x+5\right|\)= x-1
f. \(\left|x\right|+\left|2x-1\right|=x+2\)
g.\(\left|x-9\right|^{10}+\left|x-10\right|^{10}=1\)
h. \(\left|x-2014\right|^{2015}+\left|x-2015\right|^{2014}=1\)
i. \(\sqrt{x+3+4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=5\)
k. \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=x-1\)
l. \(\sqrt{x+2-4\sqrt{x-2}}+\sqrt{x+7-6\sqrt{x-2}}=1\)
m. \(\sqrt{x+8+2\sqrt{x+7}}+\sqrt{x-1-2\sqrt{x+7}}=4\)
m. \(x+\sqrt{x+\frac{1}{4}+\sqrt{x+\frac{1}{4}}}=\frac{9}{4}\)
n.\(\left(x+5\right)^4+\left(x+7\right)^4=2\)
Giải pt
Cho biểu thức \(M=\left(\frac{3}{\sqrt{x}+1}-\frac{\sqrt{x}-3}{x-1}\right):\left(\frac{x+2}{x+\sqrt{x}-2}-\frac{\sqrt{x}}{\sqrt{x}+2}\right)\). Tập hợp giá trị của x sao cho \(\left(\sqrt{x}+1\right)\times M=x-2\sqrt{x}+10+\sqrt{x-4}\)là...
cho Q= \(\frac{\sqrt{x-\sqrt{4\left(x-1\right)}}+\sqrt{x+\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}\)
a. rút gọn
b.tính GT của Q với x=2019
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 \(x=\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\)\(A=\frac{\sqrt{x}+1}{3\left(\sqrt{x}-1\right)}\)
\(\left(\frac{4\sqrt{x}}{2+\sqrt{x}}+\frac{8\sqrt{x}}{4-x}\right)\):\(\left(\frac{\sqrt{x}-1}{x-2\sqrt{x}}-\frac{2}{\sqrt{x}}\right)\)