> 数学 >
已知:
xy
x+y
=a
xz
x+z
=b
yz
y+z
=c
,且abc≠0,求x的值.
人气:240 ℃ 时间:2020-04-16 22:57:55
解答
xy
x+y
=a
xz
x+z
=b
yz
y+z
=c

x+y
xy
=
1
a
x+z
xz
=
1
b
y+z
yz
=
1
c

1
a
=
1
x
+
1
y
①,
1
b
=
1
x
+
1
z
②,
1
c
=
1
y
+
1
z
③,
①+②-③得
1
a
+
1
b
1
c
=
2
x

∴x=
2abc
bc+ac−ab
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