if x=a-b/a+b, y=b-c/b+c, z=c-a/c+a then prove that (1+x),(1+y)(1+z)=(1-x)(1-y)(1-z)
Answers
Answered by
1
If a
x−1
=bc,b
y−1
=ac,c
z−1
=ab, then find the value of xy+yz+zx−xyz.
EASY
ANSWER
We have,
a
x−1
=bc
a
a
x
=abc
a
x
=abc
a=(abc)
1/x
…(1)
Similarly,
b=(abc)
1/y
…(2)
c=(abc)
1/z
…(3)
Multiply (1),(2),(3)
abc=(abc)
1/x
.(abc)
1/y
.(abc)
1/z
abc=(abc)
1/x+1/y+1/z
∴
x
1
+
y
1
+
z
1
=1
xyz
xy+yz+zx
=1
xy+yz+zx=xyz
xy+yz+zx−xyz=0
Hence, this is the answer.
Answered by
0
Answer:
I hope this helps you
Step-by-step explanation:
We have,
a
x−1
=bc
a
a
x
=abc
a
x
=abc
a=(abc)
1/x
…(1)
Similarly,
b=(abc)
1/y
…(2)
c=(abc)
1/z
…(3)
Multiply (1),(2),(3)
abc=(abc)
1/x
.(abc)
1/y
.(abc)
1/z
abc=(abc)
1/x+1/y+1/z
∴
x
1
+
y
1
+
z
1
=1
xyz
xy+yz+zx
=1
xy+yz+zx=xyz
xy+yz+zx−xyz=0
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