Violympic toán 9
Các câu hỏi tương tự
giải pt :
a) \(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)
b0 \(4\sqrt{x+1}=x^2-5x+14\)
c) \(2x+3\sqrt{4-5x}+\sqrt{x+2}=8\)
d) \(\dfrac{x^2+x}{\sqrt{x^2+x+1}}=\dfrac{2-x}{\sqrt{x-1}}\)
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) \(\sqrt{2x+3}\cdot\sqrt[3]{x+5}=x^2+x-6\)
Giải các phương trình sau:
1. sqrt{x^2-dfrac{1}{4}+sqrt{x^2+x+dfrac{1}{4}}}dfrac{1}{2}left(2x^3+x^2+2x+1right)
2. x^2+4x+7left(x+4right)sqrt{x^2+7}
3. sqrt{x-1}+sqrt{x^3+x^2+x+1}1+sqrt{x^4-1}
4. sqrt{x^2-3x+2}+sqrt{x+3}sqrt{x-2}+sqrt{x^2+2x-3}
5. xleft(sqrt{x}+2right)left(1-sqrt{1-sqrt{x}}right)
6. 2sqrt[3]{2x-1}x^3+1
7. sqrt{x-dfrac{1}{x}}+sqrt{1-dfrac{1}{x}}x
Đọc tiếp
Giải các phương trình sau:
1. \(\sqrt{x^2-\dfrac{1}{4}+\sqrt{x^2+x+\dfrac{1}{4}}}=\dfrac{1}{2}\left(2x^3+x^2+2x+1\right)\)
2. \(x^2+4x+7=\left(x+4\right)\sqrt{x^2+7}\)
3. \(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)
4. \(\sqrt{x^2-3x+2}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)
5. \(x=\left(\sqrt{x}+2\right)\left(1-\sqrt{1-\sqrt{x}}\right)\)
6. \(2\sqrt[3]{2x-1}=x^3+1\)
7. \(\sqrt{x-\dfrac{1}{x}}+\sqrt{1-\dfrac{1}{x}}=x\)
Giải các phương trình sau:
1.
a. sqrt{x+3}-sqrt{x-4}1
b. sqrt{10-x}+sqrt{x+3}5
c. sqrt{15-x}+sqrt{3-x}6
d. sqrt{x-1}+sqrt{x+1}2
e. sqrt{4x+1}-sqrt{3x+4}1
f. sqrt{x-2sqrt{x-1}}-sqrt{x-1}1
g. sqrt{x+sqrt{2x+1}}+sqrt{x-sqrt{2x-1}}sqrt{2}
h. sqrt{x+sqrt{6x-9}}+sqrt{x-sqrt{6x-9}}sqrt{6}
i. sqrt{x^2-4x+4}+sqrt{x^2-6x+9}1
k. sqrt{x+4-4sqrt{x}}+sqrt{x+9-6sqrt{x}}1
l. sqrt{x+6-4sqrt{x+2}}+sqrt{x+11-6sqrt{x+2}}1
m. sqrt{x+2-4sqrt{x-2}}+sqrt{x+7-6sqrt{x-2}1}
n. sqrt{x}+sqrt{x+sqrt{1-x}}1
o...
Đọc tiếp
Giải các phương trình sau:
1.
a. \(\sqrt{x+3}-\sqrt{x-4}=1\)
b. \(\sqrt{10-x}+\sqrt{x+3}=5\)
c. \(\sqrt{15-x}+\sqrt{3-x}=6\)
d. \(\sqrt{x-1}+\sqrt{x+1}=2\)
e. \(\sqrt{4x+1}-\sqrt{3x+4}=1\)
f. \(\sqrt{x-2\sqrt{x-1}}-\sqrt{x-1}=1\)
g. \(\sqrt{x+\sqrt{2x+1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
h. \(\sqrt{x+\sqrt{6x-9}}+\sqrt{x-\sqrt{6x-9}}=\sqrt{6}\)
i. \(\sqrt{x^2-4x+4}+\sqrt{x^2-6x+9}=1\)
k. \(\sqrt{x+4-4\sqrt{x}}+\sqrt{x+9-6\sqrt{x}}=1\)
l. \(\sqrt{x+6-4\sqrt{x+2}}+\sqrt{x+11-6\sqrt{x+2}}=1\)
m. \(\sqrt{x+2-4\sqrt{x-2}}+\sqrt{x+7-6\sqrt{x-2}=1}\)
n. \(\sqrt{x}+\sqrt{x+\sqrt{1-x}}=1\)
o. \(\sqrt{1-\sqrt{x^2-x}}=\sqrt{x}-1\)
p. \(\sqrt{x^2+6}=x-2\sqrt{x^2-1}\)
q. \(\sqrt{2x^2+8x+6}+\sqrt{x^2-1}=2x+2\)
r. \(\sqrt{x-7}+\sqrt{9-x}=x^2-16x+66\)
s. \(\sqrt{2x-1}+\sqrt{x-2}=\sqrt{x+1}\)
t. \(\sqrt{3x+15}-\sqrt{4x-17}=\sqrt{x+2}\)
u. \(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right)\left(x^2-3x+5\right)}=4-2x\)
v. \(\sqrt{x+1}+\sqrt{x+10}=\sqrt{x+2}+\sqrt{x+5}\)
w. \(\sqrt{2x+3+\sqrt{x+2}}+\sqrt{2x+2-\sqrt{x+2}}=1+2\sqrt{x+2}\)
x. \(\sqrt{2x^2-9x+4}+3\sqrt{2x-1}=\sqrt{2x^2+21x-11}\)
y. \(\sqrt{1-x}+\sqrt{x^2-3x+2}+\left(x-2\right)\sqrt{\dfrac{x-1}{x-2}}=3\)
z. \(\left(x-2\right)\left(x+2\right)+4\left(x-2\right)\sqrt{\dfrac{x+2}{x-2}}=-3\)
2.
a. \(\dfrac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\dfrac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
b. \(\dfrac{x}{2+\dfrac{x}{2+\dfrac{x}{2+\dfrac{...}{2+\dfrac{x}{1+\sqrt{1+x}}}}}}=8\) (vế trái có 100 dấu phân thức)
c. \(\sqrt[3]{x+1}+\sqrt[3]{7-x}=2\)
d. \(\sqrt[4]{1-x}+\sqrt[4]{2-x}=\sqrt[4]{3-2x}\)
e. \(\sqrt[4]{1-x^2}+\sqrt[4]{1+x}+\sqrt[4]{1-x}=3\)
f. \(\dfrac{\sqrt[3]{7-x}-\sqrt[3]{x-5}}{\sqrt[3]{7-x}+\sqrt[3]{x-5}}=6-x\)
g. \(\sqrt[3]{x+1}+\sqrt[3]{x+2}+\sqrt[3]{x+3}=0\)
h. \(\sqrt[3]{\left(x+1\right)^2}+\sqrt[3]{\left(x-1\right)^2}+\sqrt[3]{x^2-1}=1\)
i. \(\sqrt[3]{x+1}+\sqrt[3]{x-1}=\sqrt[3]{5x}\)
k. \(\sqrt[3]{x-2}+\sqrt{x+1}=3\)
l. \(\sqrt[3]{24+x}+\sqrt{12-x}=6\)
m. \(\sqrt[3]{2-x}+\sqrt{x-1}=1\)
n. \(1+\sqrt[3]{x-16}=\sqrt[3]{x+3}\)
o. \(\sqrt[3]{25+x}+\sqrt[3]{3-x}=4\)
p. \(\sqrt[3]{x+3}-\sqrt[3]{6-x}=1\)
Làm nhanh giúp mk nhé mn ơi
1 tháng 7 2019 lúc 16:01
gpt : a) \(\frac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\frac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
b) \(\sqrt[3]{x+1}+\sqrt[3]{x+2}+\sqrt[3]{x+3}=0\)
c) \(\sqrt[4]{1-x^2}+\sqrt[4]{1+x}+\sqrt[4]{1-x}=3\)
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 \(P.\frac{x-1}{x^2+8x}< -2\)
Giải phương trình
a)\(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=x-1\)
b)\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\)
c)\(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right)\left(x+3\right)}=4-2x\)
d)\(\sqrt{x}-\sqrt{x+1}-\sqrt{x+4}+\sqrt{x+9}=0\)
1) \(2\sqrt{x+3}=x-1+4\sqrt{2x-1}\)
2) \(\sqrt[4]{x-1}+\sqrt[4]{5-x}=2\)
3) \(\sqrt[3]{1-2x}+\sqrt{x+3}=1\)
4) \(\dfrac{\sqrt{x}}{1+\sqrt{1-x}}=x^2-2x+2\)
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 \(x=\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\)\(A=\frac{\sqrt{x}+1}{3\left(\sqrt{x}-1\right)}\)
Giải phương trình:
\(a)\sqrt{x^2+2x+4}\ge x-2\\ b)x=\sqrt{x-\frac{1}{x}}+\sqrt{x+\frac{1}{x}}\\ c)\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2\sqrt{2x-5}}\\ d)x+y+z+4=2\sqrt{x-2}+4\sqrt{y-3}+6\sqrt{z-5}\\ e)\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\frac{1}{2}\left(x+y+z\right)\)