x(x-3) <0

x và x -3 trái dấu , mà x > x -3

=> x> 0 và x -3 < 0

hay 0 <x<3

\(P=\sqrt{x}+\dfrac{\sqrt[3]{2-\sqrt{3}}.\sqrt[6]{\left(2+\sqrt{3}\right)^2}-x}{\sqrt[4]{\left(\sqrt{5}-2\right)^2}.\sqrt{2+\sqrt{5}}+\sqrt{x}}\)

\(=\sqrt{x}+\dfrac{\sqrt[3]{\left(2-\sqrt{3}\right).\left(2+\sqrt{3}\right)}-x}{\sqrt{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}+\sqrt{x}}\)

\(=\sqrt{x}+\dfrac{1-x}{1+\sqrt{x}}=\sqrt{x}+1-\sqrt{x}=1\)

\(P=\left(x^2+2xy+y^2\right)+\left(x^2-2x+1\right)=\left(x+y\right)^2+\left(x-1\right)^2\ge0;\forall x;y\)

\(AD^2+AM^2=2BM^2=MN^2\)

\(2BM^2\ge2AD.AM\) (BĐT co si ) Vì AD>AM

=> \(BM^2>AD.AM\)

=>\(\dfrac{BM^2}{2}>\dfrac{AD.AM}{2}\Leftrightarrow S_{BMN}>S_{AMD}.\)

115 < 150

170 < 280