Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
Giải các hệ phương trình sau:
a) left{{}begin{matrix}4x^2-4xy-14x-3y^2+y+1005sqrt{xy}+2x+2y6sqrt{y}-8end{matrix}right.
b) left{{}begin{matrix}2x^4+3x^2y+4x^2-2y^2+3y+20sqrt{xleft(y-1right)}+2y+2sqrt{y-1}3x+2sqrt{x}+2end{matrix}right.
c) left{{}begin{matrix}x^6+3x^2-y^3-6y^2-15y-140sqrt{xy+2x-y-2}+6x-2y10end{matrix}right.
d) left{{}begin{matrix}xy+x+yx^2-2y^2xsqrt{2y}-ysqrt{x-1}2x-2yend{matrix}right.
Đọc tiếp
Giải các hệ phương trình sau:
a) \(\left\{{}\begin{matrix}4x^2-4xy-14x-3y^2+y+10=0\\5\sqrt{xy}+2x+2y=6\sqrt{y}-8\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}2x^4+3x^2y+4x^2-2y^2+3y+2=0\\\sqrt{x\left(y-1\right)}+2y+2\sqrt{y-1}=3x+2\sqrt{x}+2\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}x^6+3x^2-y^3-6y^2-15y-14=0\\\sqrt{xy+2x-y-2}+6x-2y=10\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}xy+x+y=x^2-2y^2\\x\sqrt{2y}-y\sqrt{x-1}=2x-2y\end{matrix}\right.\)
Bài 1: Rút gọn biểu thức
a) \(\left|x-2\right|+\dfrac{\sqrt{x^2-4x+4}}{x-2}\)
b) \(\sqrt{1-4a+4a^2}-2a\)
c) \(x-2y-\sqrt{x^2-4xy+4y^2}\)
d) \(x^2+\sqrt{x^4-8x^2+16}\)
giải hệ:
a) left{{}begin{matrix}sqrt{x+3y}+sqrt{x+y}2sqrt{x+y}+y-x1end{matrix}right.
b) left{{}begin{matrix}x+y+frac{1}{x}+frac{1}{y}4x^2+y^2+frac{1}{x^2}+frac{1}{y^2}4end{matrix}right.
c) left{{}begin{matrix}left(x-frac{1}{y}right)left(y+frac{1}{x}right)22x^2y+xy^2-4xy2x-yend{matrix}right.
d) left{{}begin{matrix}2x^2+xyy^2-3y+2x^2-y^23end{matrix}right.
e) left{{}begin{matrix}x^2+y^2+z^2+2xy-xz-zy3x^2+y^2-2xy-xz+zy-1end{matrix}right.
f) left{{}begin{matrix}x^2-y^2+5x-y+60x^2+left(x-yright)...
Đọc tiếp
giải hệ:
a) \(\left\{{}\begin{matrix}\sqrt{x+3y}+\sqrt{x+y}=2\\\sqrt{x+y}+y-x=1\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x+y+\frac{1}{x}+\frac{1}{y}=4\\x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=4\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}\left(x-\frac{1}{y}\right)\left(y+\frac{1}{x}\right)=2\\2x^2y+xy^2-4xy=2x-y\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}2x^2+xy=y^2-3y+2\\x^2-y^2=3\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}x^2+y^2+z^2+2xy-xz-zy=3\\x^2+y^2-2xy-xz+zy=-1\end{matrix}\right.\)
f) \(\left\{{}\begin{matrix}x^2-y^2+5x-y+6=0\\x^2+\left(x-y\right)^2=2+\sqrt{6x+7}+2\sqrt{x+y+1}\end{matrix}\right.\)
CÂU 2 :
a, Không dùng máy tính hãy so sánh : \(\dfrac{2014}{\sqrt{2015}}+\dfrac{2015}{\sqrt{2014}}\) và \(\sqrt{2014}+\sqrt{2015}\)
b, Tìm x, y, z biết : \(4x^2+2y^2+2z^2-4xy-2yz+2y-8z+10\le0\)
c, Giair phương trình : \(\sqrt{\dfrac{1}{x+3}}+\sqrt{\dfrac{5}{x+4}}=4\)
giải hệ phương trình sau
\(\left\{{}\begin{matrix}x^4-y^4=\dfrac{121x-122y}{4xy}\\x^4+14x^2y^2+y^4=\dfrac{122x-121y}{x^2+y^2}\end{matrix}\right.\)
Rút gọn:
Adfrac{sqrt[3]{x^4}+sqrt[3]{x^2y^2}+sqrt[3]{y^4}}{sqrt[3]{x^2}+sqrt[3]{xy}+sqrt[3]{y^2}}
Bdfrac{sqrt[3]{xy}left(sqrt[3]{y^2}-sqrt[3]{x^2}right)+left(sqrt[3]{x^4}-sqrt[3]{y^4}right)}{sqrt[3]{x^4}+sqrt[3]{x^2y^2}-sqrt[3]{x^3y}}.sqrt[3]{x^2}
Cleft(dfrac{xsqrt[3]{x}-2xsqrt[3]{y}+sqrt[3]{x^2y^2}}{sqrt[3]{x^2}-sqrt[3]{xy}}+dfrac{sqrt[3]{x^2y}-sqrt[3]{xy^2}}{sqrt[3]{x}-sqrt[3]{y}}right).dfrac{1}{sqrt[3]{x^2}}
Đọc tiếp
Rút gọn:
\(A=\dfrac{\sqrt[3]{x^4}+\sqrt[3]{x^2y^2}+\sqrt[3]{y^4}}{\sqrt[3]{x^2}+\sqrt[3]{xy}+\sqrt[3]{y^2}}\)
\(B=\dfrac{\sqrt[3]{xy}\left(\sqrt[3]{y^2}-\sqrt[3]{x^2}\right)+\left(\sqrt[3]{x^4}-\sqrt[3]{y^4}\right)}{\sqrt[3]{x^4}+\sqrt[3]{x^2y^2}-\sqrt[3]{x^3y}}.\sqrt[3]{x^2}\)
\(C=\left(\dfrac{x\sqrt[3]{x}-2x\sqrt[3]{y}+\sqrt[3]{x^2y^2}}{\sqrt[3]{x^2}-\sqrt[3]{xy}}+\dfrac{\sqrt[3]{x^2y}-\sqrt[3]{xy^2}}{\sqrt[3]{x}-\sqrt[3]{y}}\right).\dfrac{1}{\sqrt[3]{x^2}}\)
Rút gọn:
\(x+2y-\sqrt{\left(x^2-4xy+4y^2\right)^2}\) (x\(\ge\)2y)
Rút gọn biểu thức
1. 4x + \(\sqrt{\left(x-12\right)^2}\) (x>= 2)
2. x+2y-\(\sqrt{\left(x^2-4xy+4y^2\right)^2}\) (x>= 2y)
giúp mình với!!~~
1) \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
2) \(x+2y-\sqrt{\left(x^2-4xy+4y^2\right)^2\left(x\ge2y\right)}\)
3) 4x + \(\sqrt{\left(x-12\right)^2}\left(x\ge2\right)\)