Violympic toán 9
Các câu hỏi tương tự
Giải phương trình:
1. sqrt{2x^2+4x+7}x^4+4x^3+3x^2-2x-7
2. dfrac{4}{x}+sqrt{x-dfrac{1}{x}}x+sqrt{2x-dfrac{5}{x}}
3. dfrac{6-2x}{sqrt{5-x}}+dfrac{6+2x}{sqrt{5+x}}dfrac{8}{3}
4. x^2+1-left(x+1right)sqrt{x^2-2x+3}0
5. 2sqrt{2x+4}+4sqrt{2-x}sqrt{9x^2+16}
6. left(2x+7right)sqrt{2x+7}x^2+9x+7
Đọc tiếp
Giải phương trình:
1. \(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
2. \(\dfrac{4}{x}+\sqrt{x-\dfrac{1}{x}}=x+\sqrt{2x-\dfrac{5}{x}}\)
3. \(\dfrac{6-2x}{\sqrt{5-x}}+\dfrac{6+2x}{\sqrt{5+x}}=\dfrac{8}{3}\)
4. \(x^2+1-\left(x+1\right)\sqrt{x^2-2x+3}=0\)
5. \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2+16}\)
6. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
Rút gọn các biểu thức
a, \(A=\dfrac{\sqrt{3}-\sqrt{6}}{1-\sqrt{2}}-\dfrac{2+\sqrt{8}}{1+\sqrt{2}}\)
b, \(B=\left(\dfrac{1}{x-4}-\dfrac{1}{x+4\sqrt{x}+4}\right).\dfrac{x+2\sqrt{x}}{\sqrt{x}}\) (với x >0, x ≠ 4)
Chung minh bieu thuc sau ko phu thuoc vao gia tri cua x:
\(A=\dfrac{6x-\left(x+6\right)\sqrt{x}-3}{2\left(x-4\sqrt{x}+3\right)\left(2-\sqrt{x}\right)}-\dfrac{3}{-2x+10\sqrt{x}-12}-\dfrac{1}{3\sqrt{3}-x-2}\)
Giải phương trình
a) \(\sqrt{x-2}=\sqrt{x^2-4x+3}\)
b) \(2\left(\sqrt{\dfrac{x-1}{4}}-3\right)=2\sqrt{\dfrac{4x-4}{9}}-\dfrac{1}{3}\)
c) \(\dfrac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}\)
d) \(4+\sqrt{2x+6-6\sqrt{2x-3}}=\sqrt{2x-2+2\sqrt{2x-3}}\)
Rút gọn các biểu thức sau:
a) \(\dfrac{4}{\sqrt{11}-3}-\dfrac{5}{4+\sqrt{11}}\)
b) \(\left(\dfrac{3\sqrt{x}}{x-2\sqrt{x}}-\dfrac{2}{\sqrt{x}+3}\right):\dfrac{\sqrt{x}+13}{x+6\sqrt{x}+9}\) với x>0;x\(\ne\)4
rút gọn:
\(A=\left(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}}{x+\sqrt{x}+1}+\dfrac{1}{1-\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{2}\)
\(B=\dfrac{2x}{x+3\sqrt{x}+2}+\dfrac{5\sqrt{x}+1}{x+4\sqrt{x}-3}+\dfrac{\sqrt{x}+10}{x+5\sqrt{x}+6}\)
Giải pt
a )\(\sqrt{\dfrac{x-1}{4}}-3=\sqrt{\dfrac{4x-4}{9}}\)
b) \(\sqrt{x^2-4x+4}+\sqrt{x^2+6x+9}=x-3\)
c) \(\sqrt{\dfrac{2x-3}{x-1}}=2\)
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
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) \(\dfrac{x^2+x}{\sqrt{x^2+x+1}}=\dfrac{2-x}{\sqrt{x-1}}\)