如图所示,在三角形ABC中,已知角ACB=90度,CD垂直AB于点D,设BC=a,AC=b,CD=

2024-11-22 23:37:26
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1/a²+1/b²=1/h²???

设AB=c;
SRT△ABC=AC*BC/2=AB*CD/2
b*a=c*h
ab=ch
a²+b²=c²

1/a²+1/b²
=b²/(ab)²+a²/(ab)²
=(a²+b²)/(ab)²
=c²/(ch)²
=1/h²