QJEEM20Maac1b: JEE Main 2020 Mathematics - Class 12 JEEM20Maac1b Solution: Let x k + y k = a k , (a, k > 0 ) and d y d x + ( y x ) 1 3 = 0 …

Question

Verified Solution • 2025–26 Session moderate

Let x^k + y^k = a^k, (a, k > 0 ) and

\frac{d y}{d x} + {(\frac{y}{x})}^{\frac{1}{3}} = 0

, then k is:

Accepted Answer

x^k + y^k = a^k

\Rightarrow

kx^{k - 1} + ky^{k - 1}

\frac{d y}{d x}

= 0

\Rightarrow

\frac{d y}{d x} + {(\frac{x}{y})}^{k - 1}

= 0 ...(1)

Given

\frac{d y}{d x} + {(\frac{y}{x})}^{\frac{1}{3}} = 0

...(2)

Comparing (1) and (2), we get

k - 1 =

- \frac{1}{3}

\Rightarrow

k =

\frac{2}{3}

Step-by-Step Verified Solution