ta có S=$\frac{1}{2}$bc.sinA$S^2$=$\frac{1}{4}$$b^2$$c^2$(1-$cos^2$)
=$\frac{1}{4}$$b^2$$c^2$(1-$\frac{(b^2+c^2-a^2)^2}{4b^2c^2}$)
=$\frac{1}{16}$(2bc+$b^2$+$c^2$-$a^2$)(2bc-$b^2$-$c^2$+$a^2$)
=$\frac{1}{16}$($(b+c)^2$-$a^2$)($a^2$-$(b-c)^2$)
=$\frac{b+c+a}{2}$.$\frac{b+c-a}{2}$.$\frac{a-b+c}{2}$.$\frac{a+b-c}{2}$
=p(p-a)(p-b)(p-c)
$\Rightarrow$ đpcm.