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If a^x=b^y=c^z and abc=1 then find the v...

If `a^x=b^y=c^z` and `abc=1` then find the value of `xy+yz+zx`

A

1

B

3

C

0

D

5

Text Solution

Verified by Experts

The correct Answer is:
C
Here , ` a^(x) = b^(y) = c^(z)`
Let ` a^(x) = b^(y) = c^(z) = k`
` :. a = k^((1)/(x)) , b = k^((1)/( y)) and c = k^((1)/( z))`
`rArr abc = k ^(((1)/(x)+(1)/(y)+(1)/(z)))`
`:. abc = 1 " "` [ Given ]
` :. (1)/( x) + (1)/( y) + (1)/( z) = 0 `
` rArr xy + yz + zx = 0 `
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Knowledge Check

  • If a^(x)=b^(y)=c^(z) and abc = 1, then what is the value of xy + yz + zx ?

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  • If a^(x) =b^(y) =c^(z) and abc =1 then xy+yz+zx is equal to which of the following?

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    B
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