đpcm$\Leftrightarrow 9x^{2}+16y^{2}+25z^{2}\geq 20xy+4yz+14zx$(*)ÁD BĐT AM-GM:
$\frac{5}{3}(4x^{2}+9y^{2})\geq 2.\frac{5}{3}.\sqrt{4x^{2}.9y^{2}}=20xy$
$\frac{7}{12}(4x^{2}+36z^{2})\geq 14zx$
$y^{2}+4z^{2}\geq 4yz$
Cộng theo vế 3 BĐT trên $\Rightarrow$đpcm
Dâu''='' xra$\Leftrightarrow x=\frac{1}{2};y=\frac{1}{3};z=\frac{1}{6}$