PLZ BHAIYA LOGO, POST THE SOLUTION OR GIVE A HINT 2 SOLVE
5 Answers
qwerty
·2010-05-04 03:12:32
Let,\frac{x}{l(mb+nc-la)}=\frac{y}{m(nc+la-mb)}=\frac{z}{n(mb+la-nc)}=k
hence,
x=kl(bm+cn-al)..................(1)
y=km(al+cn-bm)..............(2)
z=kn(al+bm-cn).............(3)
now,
ax+by-cz
=k(albm+acln-a^{2}l^{2})+k(albm+bcmn-b^{2}m^{2})-k(acln+bcmn-c^{2}n^{2})
=k(2albm+c^{2}n^{2}-a^{2}l^{2}-b^{2}m^{2})
=k(c^{2}n^{2}-(al-bm)^{2})
=k(cn+al-bm)(cn+bm-al)=\frac{yx}{ml}
hence, ax+by-cz=\frac{xy}{lm}
by symmetry now, we can say,
ax+cz-by=\frac{xz}{ln}
and,
by+cz-ax=\frac{yz}{mn}
hence,
\frac{l}{x(by+cz-ax)}=\frac{m}{y(ax+cz-by)}=\frac{n}{z(ax+by-cz)}=\frac{lmn}{xyz}