N=√x+3√x+2(x≥0;x≠1)N=√x+3√x+2(x≥0;x≠1)
Xét N-32N−32:
√x+3√x+2-32√x+3√x+2−32
=2(√x+3)-3(√x+2)2(√x+2)=2(√x+3)−3(√x+2)2(√x+2)
=2√x+6-3√x-62(√x+2)=2√x+6−3√x−62(√x+2)
=-√x2(√x+2)=−√x2(√x+2)
Nhận xét
-√x≤0∀x≥0−√x≤0∀x≥0
2(√x+2)>0∀x≥02(√x+2)>0∀x≥0
→-√x2(√x+2)≤0→−√x2(√x+2)≤0
→√x+3√x+2-32≤0→√x+3√x+2−32≤0
→N≤32→N≤32