wesun365
幼苗
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证明:,∠ACB=90°;CD⊥AB.则:2S⊿ABC=AC*BC=AB*CD,即:ab=ch;
则:(ab)^2=(ch)^2,a^2b^2=c^2h^2;
故:(h^2*c^2)/(a^2b^2)=1; 又c^2=a^2+b^2.
∴[h^2(a^2+b^2)]/(a^2b^2)=1;
(h^2a^2/(a^2b^2)+(h^2b^2)/(a^2b^2)=1;
h^2/b^2+h^2/a^2=1;
上式两边同除以h^2,得:1/b^2+1/a^2=1/h^2.
1年前
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