Question

如图,已知直线y=x+1与双曲线y=k/x在第一象限交于点A,与x轴交于点C,AB⊥x轴于B.△ABC的面积为1,则AC

Answer 1

假设A(x,x+1) (x>0)

AC=√(AB^2+BC^2)

=√[AB^2+(OB+OC)^2]

=√[(x+1)^2+(x+1)^2]

=√2*(x+1)

又S△ABC=AB*BC/2

= AB *(OB+OC)/2

=(x+1)*(x+1)/2

=1

得x+1=√2

则AC=2