Violympic toán 9
Các câu hỏi tương tự
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. \(\sqrt{x-\dfrac{1}{x}}+\sqrt{1-\dfrac{1}{x}}=x\)
Rút gọn các biểu thức sau:
a) R left(dfrac{sqrt{x}+1}{sqrt{xy}+1}+dfrac{sqrt{x}left(sqrt{y}+1right)}{1-sqrt{xy}}+1right):left(1-dfrac{sqrt{x}+1}{sqrt{xy}+1}-dfrac{sqrt{x}left(sqrt{y}+1right)}{sqrt{xy}-1}right)
b) C dfrac{2sqrt{x}}{sqrt{x}+2}+dfrac{7sqrt{x}+4}{x-sqrt{x}-6}-dfrac{sqrt{x}+2}{sqrt{x}-3}
c) M left(dfrac{1}{sqrt{x}}+dfrac{sqrt{x}}{sqrt{x}+1}right):dfrac{sqrt{x}}{sqrt{x}+x}
Đọc tiếp
Rút gọn các biểu thức sau:
a) R = \(\left(\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}+\dfrac{\sqrt{x}\left(\sqrt{y}+1\right)}{1-\sqrt{xy}}+1\right):\left(1-\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}-\dfrac{\sqrt{x}\left(\sqrt{y}+1\right)}{\sqrt{xy}-1}\right)\)
b) C = \(\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{7\sqrt{x}+4}{x-\sqrt{x}-6}-\dfrac{\sqrt{x}+2}{\sqrt{x}-3}\)
c) M = \(\left(\dfrac{1}{\sqrt{x}}+\dfrac{\sqrt{x}}{\sqrt{x}+1}\right):\dfrac{\sqrt{x}}{\sqrt{x}+x}\)
1) Rút gọn biểu thức
P=\(\left(\dfrac{3x-6\sqrt{x}}{x\sqrt{x}-2x}-\dfrac{1}{2-\sqrt{x}}+\dfrac{\sqrt{x}-3}{\sqrt{x}}\right).\left(1-\dfrac{\sqrt{x}-3}{\sqrt{x}-2}\right)\)
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. 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. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
cho \(P=\left(\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{9x-1}\right)\div\left(1-\dfrac{3\sqrt{x}-2}{3\sqrt{x}+1}\right)\)
1, rút gọn P
2, tìm x để \(P\ge0\)
tính P khi \(x=-\sqrt{3-2\sqrt{2}}+\dfrac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}\)
rút gọn các biểu thức sau
a.A=\(\dfrac{4}{3+\sqrt{7}}+\sqrt{28}\)
b.B=\(\left(\dfrac{\sqrt{x}-1}{x-2\sqrt{x}+1}-\dfrac{2}{\sqrt{x}}\right):\dfrac{2-\sqrt{x}}{x-1}\) (với x>0; x\(\ne\)1; x\(\ne4\))
1) Rút gọn biểu thức
P=\(\left(\dfrac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\dfrac{x+2\sqrt{x}+4}{x-1}\right):\left(3+\dfrac{1}{\sqrt{x}-2}+\dfrac{2}{\sqrt{x}+1}\right)\)
tính P tại x=\(2\sqrt{2}\)
\(P=\dfrac{\sqrt{\sqrt{\dfrac{x-1}{x+1}+\sqrt{\dfrac{x+1}{x-1}}}}-2\left(2x+\sqrt{x^2+1}\right)}{\sqrt{\left(x+1\right)^3}-\sqrt{\left(x-1\right)^3}}\)