若a，b∈R,且a+b+3=ab,則ab的取值范圍是?要詳細過程,謝謝!!!!!!!

熱心網(wǎng)友

若a，b∈R,且a+b+3=ab,則ab的取值范圍是?解:設(shè)ab=t.∵a+b+3=ab∴a(a+b+3)=at∴a^+t+3a=at∴a^+(3-t)a+t=0a∈R△=(3-t)^-4t≥0∴t^-10t+9≥0t≤1或t≥9

熱心網(wǎng)友

ab=a+b+3≥2√ab+3ab-2√ab-3=(√ab+1)(√ab-3)≥0∵√ab+1≥1＞0,∴(√ab-3)≥0--√ab≥3---ab≥9