\(\dfrac{x^5-2x^4+2x^3-4x^2-3x+6}{x^2+2x-8}\le0\)
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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
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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. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
Giải phương trình:
1, \(x^2+2x\sqrt{x-\dfrac{1}{x}}=3x+1\)
2, \(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{16x-4x^2-15}\)
3, \(7\sqrt{3x-7}+\left(4x-7\right)\sqrt{7-x}=32\)
Giải phương trình:
1, sqrt{x^2+2x}+sqrt{2x-1}sqrt{3x^2+4x+1}
2, x^3-3x^2+2sqrt{left(x+2right)^3}-6x0
3, 2x^3-x^2-3x+1sqrt{x^5+x^4+1}
4, 5sqrt{x^4+8x}4x^2+8
5, left(x^2+4right)sqrt{2x+4}3x^2+6x-4
6, left(x^2-6x+11right)sqrt{x^2-x+1}2left(x^2-4x+7right)sqrt{x-2}
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Giải phương trình:
1, \(\sqrt{x^2+2x}+\sqrt{2x-1}=\sqrt{3x^2+4x+1}\)
2, \(x^3-3x^2+2\sqrt{\left(x+2\right)^3}-6x=0\)
3, \(2x^3-x^2-3x+1=\sqrt{x^5+x^4+1}\)
4, \(5\sqrt{x^4+8x}=4x^2+8\)
5, \(\left(x^2+4\right)\sqrt{2x+4}=3x^2+6x-4\)
6, \(\left(x^2-6x+11\right)\sqrt{x^2-x+1}=2\left(x^2-4x+7\right)\sqrt{x-2}\)
Giải phương trình:
1, left(x^2+x+1right)left(x^4+2x^3+7x^2+26x+37right)5left(x+3right)^3
2, left(x+1right)^3+left(x+3right)^3+6left(x+1right)left(x+7right)left(x+3right)8left(x+2right)^3
3, x^3+left(x-1right)^3+3xleft(x-1right)left(x^4+xright)left(2x-1right)^3
4, dfrac{left(x+1right)^3}{3x+1}+dfrac{x^3+5x+2}{x^3+2x+1}x+3
5, dfrac{5x^3+x^2+x+1}{4x^2+1}+dfrac{6left(4x^2+1right)}{x^3+x^2+1}x+7
6, left(x^2-4x+1right)^3+left(8x-x^2+4right)^3+left(x-5right)^3125x^3
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Giải phương trình:
1, \(\left(x^2+x+1\right)\left(x^4+2x^3+7x^2+26x+37\right)=5\left(x+3\right)^3\)
2, \(\left(x+1\right)^3+\left(x+3\right)^3+6\left(x+1\right)\left(x+7\right)\left(x+3\right)=8\left(x+2\right)^3\)
3, \(x^3+\left(x-1\right)^3+3x\left(x-1\right)\left(x^4+x\right)=\left(2x-1\right)^3\)
4, \(\dfrac{\left(x+1\right)^3}{3x+1}+\dfrac{x^3+5x+2}{x^3+2x+1}=x+3\)
5, \(\dfrac{5x^3+x^2+x+1}{4x^2+1}+\dfrac{6\left(4x^2+1\right)}{x^3+x^2+1}=x+7\)
6, \(\left(x^2-4x+1\right)^3+\left(8x-x^2+4\right)^3+\left(x-5\right)^3=125x^3\)
Giải phương trình vô tỉ:
a) \(4x^2-4x-10=\sqrt{8x^2-6x-10}\)
b) \(\sqrt{\left(x+1\right)\left(2-x\right)}=1+2x-2x^2\)
c) \(\sqrt{3x+8+6\sqrt{3x-1}}+\sqrt{3x+8-6\sqrt{3x-1}}=3x+4\)
d) \(2x\sqrt{x^2-x+1}+4\sqrt{3x+1}=2x^2+2x+6\)
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 các phương trình sau:
a, \(\left(x-3\right)^2+x^4=-y^2+6y-4\)
b, \(\sqrt{2x-3}+\sqrt{5-2x}-x^2+4x-6=0\)
c, \(4+4x-x^2=|x-1|+|x-2|+|2x-3|+|4x-14|\)
d, \(x^2-2x+3=\sqrt{2x^2-x}+\sqrt{1+3x-3x^2}\)
giải phương trình
\(3\sqrt{x}+\dfrac{3}{2\sqrt{x}}< 2x+\dfrac{1}{2x}-7\)
\(\left(4x-1\right)+\sqrt{x^2+1}=2x^2+2x+1\)
\(\dfrac{\sqrt{-3x^2+x+4}+2}{x}< 2\)
Giải phương trình:
1, left(x+3right)left(3x^4+8x^2+12x+21right)5left(x^2+1right)^3
2, 3left(x^2+2x-1right)^2-2left(x^2+3x-1right)^2+5x^20
3, dfrac{x^2+x+1}{x+1}+dfrac{x^2+2x+2}{x+2}-dfrac{x^2+3x+3}{x+3}-dfrac{x^2+4x+4}{x+4}0
4, left(dfrac{x+6}{x-6}right)left(dfrac{x+4}{x-4}right)^2+left(dfrac{x-6}{x+6}right)left(dfrac{x+9}{x-9}right)^22.dfrac{x^2+36}{x^2-36}
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Giải phương trình:
1, \(\left(x+3\right)\left(3x^4+8x^2+12x+21\right)=5\left(x^2+1\right)^3\)
2, \(3\left(x^2+2x-1\right)^2-2\left(x^2+3x-1\right)^2+5x^2=0\)
3, \(\dfrac{x^2+x+1}{x+1}+\dfrac{x^2+2x+2}{x+2}-\dfrac{x^2+3x+3}{x+3}-\dfrac{x^2+4x+4}{x+4}=0\)
4, \(\left(\dfrac{x+6}{x-6}\right)\left(\dfrac{x+4}{x-4}\right)^2+\left(\dfrac{x-6}{x+6}\right)\left(\dfrac{x+9}{x-9}\right)^2=2.\dfrac{x^2+36}{x^2-36}\)