Math, asked by Soutrick05, 6 months ago

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 KvenuTecnoGamer
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 siyonashekhawat
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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