作业帮已知a/b=c/d,求证：a²+b²/ab=c²+d²/cd
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/15 17:04:15
x){}KlStmlzYjʆIZ?(J
%$Sf~
dnl 3mmShik$&ij@0 M[(KEYjʓS
SPBȦ
KbU
>p
l m@C 3mS|6׆aZL@ir H I й
已知a/b=c/d,求证：a²+b²/ab=c²+d²/cd
已知a/b=c/d,求证：a²+b²/ab=c²+d²/cd
已知a/b=c/d,求证：a²+b²/ab=c²+d²/cd
令a/b=c/d=k,则a=bk c=dk
(a²+b²)/(ab)=(b²k²+b²)/(b²k)=b²(k²+1)/(b²k)=(k²+1)/k
(c²+d²)/(cd)=(d²k²+d²)/(d²k)=d²(k²+1)/(d²k)=(k²+1)/k
(a²+b²)/(ab)=(c²+d²)/(cd)
a/b=c/d
则 b/a=d/c
a/b+b/a=c/d+d/c
(a²+b²)/ab=(c²+d²)/cd
令a/b=c/d=k，则a=bk c=dk
(a²+b²)/(ab)=(b²k²+b²)/(b²k)=b²(k²+1)/(b²k)=(k²+1)/k
(c²+d²)/(cd)=(d²k²+d²)/(d²k)=d²(k²+1)/(d²k)=(k²+1)/k
(a²+b²)/(ab)=(c²+d²)/(cd)