例二怎么解答

更新时间2022-03-19 12:17:19

怎么解

“例题”是给学生的示范，“习题”是给学生的练习。

连例题和习题的区别都不知，编书人的素质可想而知。

∵ ∆ABC，∴ AB/sinC=AC/sinB。∴ AB/AC=sinC/sinB。

∵ AD是∆ABC的内角平分线，∴ AB/AC=BD/CD。

∵ S(ABD)：S(ACD)=2，

∴ 2=0.5AB*BDsinB/(0.5AC*CDsinC)

=(AB/AC)(BD/CD)(sinB/sinC)

=(sinC/sinB)²(sinB/sinC)=sinC/sinB

∴ sinB/sinC=1/2

∵ BD/CD=AB/AC=sinC/sinB=2

∴ AB=2AC，BD=2CD=2(√2)/2=√2★

cos∠ADB=(BD²+AD²-AB²)/(2BD*AD)

=[(√2)²+1²-4AC²]/[2(√2)*1]

=(3-4AC²)/(2√2)

cos∠ADC=(CD²+AD²-AC²)/(2CD*AD)

=(1/2+1-AC²)/(2*0.5√2*1)

=(3/2-AC²)/√2=(3-2AC²)/(2√2)

∵ ∠ADB+∠ADC=180°

∴ cos∠ADB+cos∠ADC=0

∴ (3-4AC²)/(2√2)+(3-2AC²)/(2√2)=0

∴ (3-4AC²)+(3-2AC²)=0

∴ AC=1★