\(\sqrt{x}=10-2\sqrt{y}\)
\(\Rightarrow x+y=\left(10-2\sqrt{y}\right)^2+y=5y-40\sqrt{y}+100\)
\(=5\left(\sqrt{y}-4\right)^2+20\ge20\)
cho \(\sqrt{x}+2\sqrt{y}=10.CMR:x+y\ge20\)
cho \(\sqrt{x}+2\sqrt{y}=10\)chứng minh rằng \(x+y\ge20\)
Cho \(\sqrt{x}+2\sqrt{y}=10.\) . Chứng minh \(x+y\)\(\ge20\)
Cho x, y, z >0 và xyz=100
CMR: \(\frac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+10}+\frac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\frac{10\sqrt{z}}{\sqrt{xz}+\sqrt{z}+10}=1\)
cho x,y,z >0. CMR
\(\frac{x}{\sqrt{x}+\sqrt{y}}+\frac{y}{\sqrt{y}+\sqrt{z}}+\frac{z}{\sqrt{x}+\sqrt{z}}=\frac{y}{\sqrt{x}+\sqrt{y}}+\frac{z}{\sqrt{y}+\sqrt{z}}+\frac{x}{\sqrt{x}+\sqrt{z}}\)
10 tik nha !!!!!!!!
Cho x,y,a tm:
\(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{y^4x^2}}=a\)
CMR: \(\sqrt[3]{a^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)
Cho x,y thỏa mãn ( \(\sqrt{2+x^2}\) - x) (y + \(\sqrt{2+y^2}\)) = 2. CMR: x=y
Cho x, y thoả mãn : x2 + y2 - 4x - 2 = 0. CMR : \(10-4\sqrt{6}\le x^2+y^2\le10+4\sqrt{6}\)
Cho x,y,z>0 và x+y+z=1.CMR:\(\sqrt{x^2+\dfrac{1}{y^2}}+\sqrt{y^2+\dfrac{1}{z^2}}\sqrt{z^2+\dfrac{1}{x^2}}>=\sqrt{82}\)
