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If x^(3) + 3 (ky)^(3) = k^(3) and (dy)/(...

If `x^(3) + 3 (ky)^(3) = k^(3)` and `(dy)/(dx) + (x^(2))/(24 y^(2)) = 0`, then k is (where k `gt` 0)

A

`(3)/(2)`

B

2

C

`(2)/(3)`

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
Differentiating both sides
`x^(3) + 3 (ky)^(3) = k^(3)`, `3x^(2) + 9k^(3) y^(2) (dy)/(dx) = 0`
`(dy)/(dx) = - (x^(2))/(3k^(3) y^(2))`
On comparing with given equation `- (1)/(3k^(3)) = - (1)/(24)`, `k^(3) = 8 implies k = 2`
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