∵x，y∈R+，且4x+1+12y+1＝1，∴x+2y=（x+1）+（2y+1）-2=(4x+1+12y+1)[(x+1)+(2y+1)]−2=3+(x+1)2y+1+4(2y+1)x+1≥3+2x+12y+1×4(2y+1)x+1=7．当且仅当4x+1+12y+1＝1，x+12y+1＝4(2y+1)x+1，即x＝5y＝1时取等号．...