Violympic toán 9
Các câu hỏi tương tự
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) \(4+\sqrt{2x+6-6\sqrt{2x-3}}=\sqrt{2x-2+2\sqrt{2x-3}}\)
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. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
28 tháng 11 2019 lúc 23:30
Giải các pt sau:
a) sqrt{x+8}+frac{9x}{sqrt{x+8}}-6sqrt{x}0
b) x^4-2x^3+sqrt{2x^3+x^2+2}-20
c) 3xsqrt[3]{x+7}left(x+sqrt[3]{x+7}right)7x^3+12x^2+5x-6
d) 4x^2+left(8x-4right)sqrt{x}-13x+2sqrt{2x^2+5x-3}
e) 16x^2+19x+7+4sqrt{-3x^2+5x+2}left(8x+2right)left(sqrt{2-x}+2sqrt{3x+1}right)
f) left(5x+8right)sqrt{2x-1}+7xsqrt{x+3}9x+8-left(x+26right)sqrt{x-1}
g) sqrt[3]{3x+1}+sqrt[3]{5-x}+sqrt[3]{2x-9}-sqrt[3]{4x-3}0
Đọc tiếp
Giải các pt sau:
a) \(\sqrt{x+8}+\frac{9x}{\sqrt{x+8}}-6\sqrt{x}=0\)
b) \(x^4-2x^3+\sqrt{2x^3+x^2+2}-2=0\)
c) \(3x\sqrt[3]{x+7}\left(x+\sqrt[3]{x+7}\right)=7x^3+12x^2+5x-6\)
d) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}\)
e) \(16x^2+19x+7+4\sqrt{-3x^2+5x+2}=\left(8x+2\right)\left(\sqrt{2-x}+2\sqrt{3x+1}\right)\)
f) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+8-\left(x+26\right)\sqrt{x-1}\)
g) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
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 phương trình:
1, \(4\sqrt{x+3}+\sqrt{19-3x}=x^2+2x+9\)
2, \(\sqrt{3x-8}-\sqrt{x+1}=\dfrac{2x-11}{5}\)
3, \(\sqrt{x+\dfrac{3}{x}}=\dfrac{x^2+7}{2\left(x+1\right)}\)
Giải phương trình vô tỉ:
a) 1+frac{2}{3}sqrt{x-x^2}sqrt{x}+sqrt{1-x}
b) sqrt{2x+3}+sqrt{x+1}3x+2sqrt{2x^2+5x+3}-2
c) sqrt{7x+7}+sqrt{7x-6}+2sqrt{49x^2+7x-42}181-4x
d) frac{sqrt{x+4}+sqrt{x-4}}{2}x+sqrt{x^2-16}-6
e) 5sqrt{x}+frac{5}{2sqrt{x}}2x+frac{1}{2x}+4
g) sqrt{3x-2}+sqrt{x-1}4x-9+2sqrt{3x^2-5x+2}
Đọc tiếp
Giải phương trình vô tỉ:
a) \(1+\frac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
b) \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-2\)
c) \(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-4x\)
d) \(\frac{\sqrt{x+4}+\sqrt{x-4}}{2}=x+\sqrt{x^2-16}-6\)
e) \(5\sqrt{x}+\frac{5}{2\sqrt{x}}=2x+\frac{1}{2x}+4\)
g) \(\sqrt{3x-2}+\sqrt{x-1}=4x-9+2\sqrt{3x^2-5x+2}\)
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
1) dfrac{x-3x^2}{2}+sqrt{2x^4-x^3+7x^2-3x+3}2
2) 1+sqrt{dfrac{x-2}{1-x}}dfrac{2x^2-2x+1}{x^2-2x+2}
3) x+y+z+dfrac{3}{x-1}+dfrac{3}{y-1}+dfrac{3}{z-1}2left(sqrt{x+2}+sqrt{y+2}+sqrt{z+2}right) với x ,y ,z 1
4) sqrt[3]{x+6}+x^27-sqrt{x-1}
5) x^4-2x^3+x-sqrt{2left(x^2-xright)}0
Đọc tiếp
1) \(\dfrac{x-3x^2}{2}+\sqrt{2x^4-x^3+7x^2-3x+3}=2\)
2) \(1+\sqrt{\dfrac{x-2}{1-x}}=\dfrac{2x^2-2x+1}{x^2-2x+2}\)
3) \(x+y+z+\dfrac{3}{x-1}+\dfrac{3}{y-1}+\dfrac{3}{z-1}=2\left(\sqrt{x+2}+\sqrt{y+2}+\sqrt{z+2}\right)\) với x ,y ,z > 1
4) \(\sqrt[3]{x+6}+x^2=7-\sqrt{x-1}\)
5) \(x^4-2x^3+x-\sqrt{2\left(x^2-x\right)}=0\)
Giải phương trình:
1, 3x^2+6x-3sqrt{dfrac{x+7}{3}} (2 cách khác nhau )
2, left(sqrt{3x+1}-sqrt{x-2}right)left(sqrt{3x^2+7x+2}+4right)4x-2
3, sqrt{-3x-1}+sqrt{9x^2+9x+3}-9x^2-6x
4, sqrt{x^2+x-6}+3sqrt{x-1}sqrt{5x^2-1}
5, left(sqrt{x+4}+2right)left(x+2sqrt{x-5}+1right)6x
6, sqrt{5-x^4}-sqrt[3]{3x^2-2}1
7, 3x^2+11+sqrt{x-2}+sqrt{2x+3}14x
8, sqrt{x-sqrt{x-sqrt{x-sqrt{x-7}}}}7
9, sqrt{2x^2-1}+3xsqrt{x^2-1}3x^3+2x^2-9x-7 ( với x0 )
Đọc tiếp
Giải phương trình:
1, \(3x^2+6x-3=\sqrt{\dfrac{x+7}{3}}\) (2 cách khác nhau )
2, \(\left(\sqrt{3x+1}-\sqrt{x-2}\right)\left(\sqrt{3x^2+7x+2}+4\right)=4x-2\)
3, \(\sqrt{-3x-1}+\sqrt{9x^2+9x+3}=-9x^2-6x\)
4, \(\sqrt{x^2+x-6}+3\sqrt{x-1}=\sqrt{5x^2-1}\)
5, \(\left(\sqrt{x+4}+2\right)\left(x+2\sqrt{x-5}+1\right)=6x\)
6, \(\sqrt{5-x^4}-\sqrt[3]{3x^2-2}=1\)
7, \(3x^2+11+\sqrt{x-2}+\sqrt{2x+3}=14x\)
8, \(\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-7}}}}=7\)
9, \(\sqrt{2x^2-1}+3x\sqrt{x^2-1}=3x^3+2x^2-9x-7\) ( với \(x>0\) )