由原式得,
k>(a^2+b^2+2ab+a^2+b^2+16c^2+2ab+8ac+8bc)*(1/(ab)+1/(ac)+1/(bc))
=2(5a/b+5b/a+12c/b+3b/c+12c/a+3a/c+8c^2/(ab)+b^2/(ac)+a^2/(bc)+10)
≥2(5*2*√(a/b*b/a)+2*√(12c/b*3b/c)+2*√(12c/a*3a/c)+3*(8c^2/(ab)*b^2/(ac)*a^2/(bc))^(1/3))
=2*(10+12+12+6+10)
=100
当且仅当a=b=2c时,k取最小值100