(lg5)^2+lg2×lg50
=(lg5)^2+lg2×(lg5+lg10)
=(lg5)^2+lg2×(lg5+1)
=(lg5)^2+lg2×lg5+lg2
=lg5×(lg5+lg2)+lg2
=lg5×lg10+lg2
=lg5×1+lg2
=lg5+lg2
=lg10
=1