Question

求解第8题

Answer 1

令y=0得
x=-3或x=1
A(-3,0) B(1,0) ,C(0,√3)
AC=√(9+3)=2√3
AD=√2 /2*AC=2√3*√2 /2=√6
过点D作MN//AB,MN交y轴于点F,AE垂直于MN于点E,
∵∠ADC=90
∴∠ADE+∠CDF=90
∵∠DCF+∠CDF=90,∠ADE+∠CDF=90
∠DCF+∠CDF=∠ADE+∠CDF=90
∴∠DCF=∠ADE
∵∠AED=∠CFD=90 ,∠DCF=∠ADE,AD=CD
∴RT△ADE≌RT△CDF(AAS)
∴AE=DF,DE=CF
∵AE=m,DE=CF=√3-m
∵AE^2+DE^2=AD^2
m^2+(√3-m)^2=(√6)^2
2m^2-2√3m-3=0
m=(3+2√3)/2 或m=(-3+2√3)/2