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BITSAT2013MathematicsApplication of DerivativesActual

If a² x⁴+b² y⁴=c⁴ , then the maximum value of xy is

Options

  1. Ac ab
  2. Bc² 2 a b
  3. Cc 2 ab
  4. Dc² 2 a b

Correct answer

D. c² 2 a b

Step-by-step solution

If the sum of two positive quantities is a constant, then their product is maximum, when they are equal. a ² x ⁴ b ² y ² is maximum when a² x⁴=b² y⁴= 1 2 (a² x⁴= 1 2 (a² x⁴+b² y⁴ )= c⁴ 2 . maximum value of a² x⁴ b² y⁴= c⁴ 2 c⁴ 2 = c⁸ 4 Maximum value of x y= ( c⁸ 4 a² b² )^ 1 / 4 = c² 2 a b

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