Question

已知a,b,c为实数,且a+b/ab=3,b+c/ab=4,c+a/ca=5 1.求1/a+1/b+1/c的值 2.求a

Answer 1

{(a+b)/(ab)=3

{(b+c)/(bc)=4

{(c+a)/(ca)=5

整理得：

{1/a+1/b=3 ①

{1/b+1/c=4 ②

{1/c+1/a=5 ③

是式相加得

2(1/a+1/b+1/c)=12 ④

(1)由①得1/a+1/b+1/c=6 ⑤

(2)由上式得(bc+ca+ab)/(abc)=6

所以abc/(ab+bc+ca)=1/6

(3)⑤-②得1/a=2

⑤-③得1/b=1

⑤-①得1/c=3

所以a=2,b=1,c=3