Các câu hỏi tương tự
cho cac so thuc x va y thoa man
\(\left(x^2+\sqrt{1+x^2}\right)\left(y^2+\sqrt{1+y^2}\right)=1\)1
chung minh x+y=0
1. Tim x,y,z biet: \(\frac{1}{2}\left(x+y+z\right)-3=\sqrt{x-2}+\sqrt{y-3}+\sqrt{z-4}\)
2. Chox,y,z > 0 thoa man \(x+y+z+\sqrt{xyz}=4\) . Tinh \(A=\sqrt{x\left(4-y\right)\left(4-z\right)+\sqrt{y\left(4-z\right)\left(4-x\right)}+\sqrt{z\left(4-x\right)\left(4-y\right)}-\sqrt{xyz}}\)
a) tim GTNN, GTLN cua A = \(\sqrt{\left(x-1\right)}\)+\(\sqrt{\left(5-x\right)}\)
b) cho cac so duong x,y thoa man x+y>=3
CM: x+y+1/2x+2/y>=9/2
a) tim GTNN cua A = \(\sqrt{\left(x-1\right)}\)+ \(\sqrt{\left(5+x\right)}\)
b) cho cac so dang x, y thoa man x+y>=3
CM: x+y + 1/2x+ 2/y >= 9/2
cho x, y\(\in R\)thoa man \(\left(X+\sqrt{x^2+1}\right)\left(y+\sqrt{y^2+1}\right)=1\)
Tim min, max cua M=\(10x^4+8y^4-15xy+6x^2+5y^2+2017\)
26 tháng 10 2021 lúc 17:16
Ghpt:
a) \(\left\{{}\begin{matrix}\left(4x^2+1\right).x+\left(y-3\right)\sqrt{5-2y}=0\\4x^2+y^2+2\sqrt{3-4x}=7\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^2+y^2=5\\\sqrt{y-1}\left(x+y-1\right)=\left(y-2\right)\sqrt{x+y}\end{matrix}\right.\)
Cho x,y dương thỏa mãn \(\sqrt{x}+\sqrt{y}-2>=0\)
CMR \(xy\left(\sqrt{x}+\sqrt{y}-2\right)+x^2\left(\sqrt{x}-1\right)+y^2\left(\sqrt{y}-1\right)>=0\)
Rút gọn các biểu thức sau:a)frac{sqrt{108x^3}}{sqrt{12x}}left(x0right)b)frac{sqrt{13x^4y^6}}{sqrt{208x^6y^6}}left(x 0;yne0right)c)frac{xsqrt{x}+ysqrt{y}}{sqrt{x}+sqrt{y}}-left(sqrt{x}+sqrt{y}right)^2d) sqrt{frac{x-2sqrt{x}+1}{x+2sqrt{x}+1}}left(xgeright)e)frac{x-1}{sqrt{y}-1}.sqrt{frac{left(y-2sqrt{y}+1right)^2}{left(x-1right)^4}}left(y0;xne1;yne1right)
Đọc tiếp
Rút gọn các biểu thức sau:
a)\(\frac{\sqrt{108x^3}}{\sqrt{12x}}\left(x>0\right)\)
b)\(\frac{\sqrt{13x^4y^6}}{\sqrt{208x^6y^6}}\left(x< 0;y\ne0\right)\)
c)\(\frac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-\left(\sqrt{x}+\sqrt{y}\right)^2\)
d) \(\sqrt{\frac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}\left(x\ge\right)\)
e)\(\frac{x-1}{\sqrt{y}-1}.\sqrt{\frac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}\left(y>0;x\ne1;y\ne1\right)\)
rút gọn Bt
a)\(\frac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}-\left(\sqrt{x}-\sqrt{y}\right)^2\)
b)\(\frac{x-y}{\sqrt{y}-1}.\sqrt{\frac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}\left(x\ne1,y\ne1,y>0\right)\)