若a，b∈R,且a+b+3=ab,则ab的取值范围是?要详细过程,谢谢!!!!!!!
热心网友
若a，b∈R,且a+b+3=ab,则ab的取值范围是?解:设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
热心网友
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
若a，b∈R,且a+b+3=ab,则ab的取值范围是?要详细过程,谢谢!!!!!!!
若a，b∈R,且a+b+3=ab,则ab的取值范围是?解:设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
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