1.\(N=x^2+\frac{1000}{x}+\frac{1000}{x}\ge3\sqrt[3]{\frac{x^2.1000.1000}{x^2}}\)
\(\Rightarrow N\ge300\)
Dấu "=" xảy ra \(\Leftrightarrow x^3=1000\Leftrightarrow x=10\)
2.\(P=\left(5x+\frac{12}{x}\right)+\left(3y+\frac{16}{y}\right)\ge2\sqrt{60}+2\sqrt{48}=4\sqrt{15}+8\sqrt{3}\)
Dấu "=" xảy ra \(\Leftrightarrow5x=\frac{12}{x};3y=\frac{16}{y}\Leftrightarrow x=\sqrt{\frac{12}{5}};y=\frac{4\sqrt{3}}{3}\)
\(\)