ĐKXĐ: ...
\(VT\le\sqrt{2\left(x-3+5-x\right)}=2\)
\(VP=\left(y+\sqrt{2019}\right)^2+2\ge2\)
\(\Rightarrow VP\ge VT\)
Dấu "=" xảy ra khi và chỉ khi:
\(\left\{{}\begin{matrix}x-3=5-x\\y+\sqrt{2019}=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=4\\y=-\sqrt{2019}\end{matrix}\right.\)
Cho x,y,z >0 thỏa x+y+z=\(\sqrt{2021}\)
Tìm Min:
\(P=\sqrt{\left(x+y\right)\left(y+z\right)\left(z+x\right)}.\left(\dfrac{\sqrt{y+z}}{x}+\dfrac{\sqrt{z+x}}{y}+\dfrac{\sqrt{x+y}}{z}\right)\)
\(\sqrt{x+2018}+\sqrt{y-2019}+\sqrt{z-2}=\dfrac{1}{2}\left(x+y+z\right)\)
1) rút gọn biểu thức sau :
a) \(\dfrac{x+2\sqrt{x}-3}{\sqrt{x}-1}\) b) \(\dfrac{4y+3\sqrt{y}-7}{4\sqrt{y}+7}\) c ) \(\dfrac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)
d) \(\dfrac{x-3\sqrt{x}-4}{x-\sqrt{x}-12}\) e) \(\dfrac{1+\sqrt{x}+\sqrt{y}+\sqrt{xy}}{1+\sqrt{y}}\) ( với x>0 , y>0 )
f) \(\sqrt{8-2\sqrt{15}}+\sqrt{5}+\sqrt{3}\) g) \(\sqrt{9-2\sqrt{4}}-\sqrt{9+2\sqrt{14}}\)
1. Tính:
\(\sqrt{\dfrac{x-1+\sqrt{2x-3}}{x+2-\sqrt{2x+3}}}\)
2. Chứng minh:
a) \(\dfrac{\left(3\sqrt{xy}-6y.2x\sqrt{y}+4y\sqrt{x}\right)\left(3\sqrt{y}+2\sqrt{xy}\right)}{y\left(\sqrt{x}-2\sqrt{y}\right)\left(y-4x\right)}=1\)
b) \(\left(\sqrt{x}-\sqrt{y}-\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right)\left(\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}}+\dfrac{y}{\sqrt{x}-\sqrt{y}}-\dfrac{2\sqrt{xy}}{xy}\right)=\sqrt{x}+\sqrt{y}\)
Rút gọn : a) \(\dfrac{a\sqrt{b}-b\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\sqrt{ab}\)
b)\(\dfrac{x+4y-4\sqrt{xy}}{\sqrt{x}-2\sqrt{y}}+\dfrac{y+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\left(x\ge0;y\ge0;x\ne4y\right)\)
c)\(\dfrac{x+4\sqrt{x}+4}{\sqrt{x}+2}+\dfrac{4-x}{\sqrt{x}-2}\left(x\ge0;x\ne4\right)\)
d)\(\dfrac{9-x}{\sqrt{3x}+3}-\dfrac{9-6\sqrt{x}+x}{\sqrt{x}-3}\)
e)\(\dfrac{\left(\sqrt{x}-\sqrt{y}\right)^2+4\sqrt{xy}}{\sqrt{x}+\sqrt{y}}-\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}\)
g)\(\left(2-\dfrac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\left(2-\dfrac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)với\) a, b \(\ge\)0 , a \(\ne\)9; b\(\ne\)25
Mọi người giúp tớ với , cảm ơn nhiều nhiều ạ !!
Tìm x, y, z biết:
\(\sqrt{x+1}+\sqrt{y-3}+\sqrt{z-1}=\dfrac{1}{2}\left(x+y+z\right)\)
Giải phương trình :
a,\(x^2+\sqrt{x+2021}=2021\)
b,\(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
Mấy bạn giúp mình bài này nha!
1) Tính A=(\(\sqrt{6}+\sqrt{2}\))*(\(\sqrt{3}-2\))*\(\sqrt{2+\sqrt{3}}\)
2) Cho x=4+\(\sqrt{10}\)
Tính A=\(\sqrt{3x+\sqrt{6x-1}}+\sqrt{3x-\sqrt{6x-1}}\)
3) Cho \(\sqrt{x}+\sqrt{y}-\sqrt{z}=0\)
CMR: \(\dfrac{1}{x+y-z}+\dfrac{1}{y+z-x}+\dfrac{1}{z+x-y}=0\)
4) Cho (\(\sqrt{x^2+5}+x\))*(\(\sqrt{y^2+5}+y\))=4
CMR: x+y=0
Tìm x, y
a) \(\sqrt{1-x}+\sqrt{4+x}=3\)
b) \(x^2+4x+5=2\sqrt{2x+3}\)
c) \(2\left(x\sqrt{y-4}+y\sqrt{x-4}\right)=xy\)
