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Let x^(k)+y^(k) , (a,k gt 0) and (dy)/(d...

Let `x^(k)+y^(k) , (a,k gt 0) and (dy)/(dx) +((y)/(x))^((1)/(3)) =0` then k is :

A

`1/3`

B

`2/3`

C

`-1/3`

D

`-2/3`

Text Solution

Verified by Experts

The correct Answer is:
D
`kx ^(k-1) + ky^(k-1) (dy)/(dx) =0`
`(dy)/(dx) =-(k (x ^(k-1)))/(k (y ^(k-1)))+ " implies(dy)/(dx) =- ((y)/(x)) ^(1-k)`
now by comparing `1 -k =5/3`
`k =1 - 5/3 implies k =-2/3`
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