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Solution:
x^k + y^k = a^k
diffrentiate w.r.t x of both side we get
k x^(k -1) + ky^(k -1)( dy/dx) = 0
⇒ ( dy/dx) = -(x/y)^k -1
⇒ dy/dx + (y/x)^1 - k =0
⇒ ( 1 - k ) = 1/3
⇒ k =2/3 Ans