câu 5) [tex]\sqrt{\left (1+x^4 \right )(1+\frac{1}{16})}+\sqrt{\left (1+y^4 \right )(1+\frac{1}{16})}\geqslant\sqrt{\left ( 1+\frac{x^2}{4} \right )^2}+\sqrt{\left ( 1+\frac{y^2}{4} \right )^2}=2+\frac{x^2+y^2}{4}\geqslant \frac{(x+y)^2}{8}+2[/tex]
mà [tex](x+2)(y+2)=\frac{25}{4}\leqslant \frac{(x+y+4)^2}{4}<=>x+y+4\geqslant 5=>x+y\geqslant 1[/tex]
=>[tex]\sqrt{\frac{17}{16}}P\geqslant \frac{1}{8}+2=\frac{17}{8}=>P\geqslant \frac{\sqrt{17}}{2}[/tex]