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MHT CET202314 May 2023Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If ⁻¹ x- ⁻¹ y 3 = , where -1 x 1 , -3 y 3, x y 3 , then for all x, y , 9 x^2-6 x y +y^2 is equal to

Options

  1. A^2
  2. B3 ^2
  3. C9 ^2
  4. D4 9 ^2

Correct answer

C. 9 ^2

Step-by-step solution

If ⁻¹ x a - ⁻¹ y b = , then x^2 a ^2 - 2 x y ab + y^2 ~b ^2 = ^2 Given, ⁻¹ x- ⁻¹ y 3 = Here, a =1, ~b =3 aligned & x^2 1^2 - 2 x y (1)(3) + y^2 3^2 = ^2 & x^2- 2 x y 3 + y^2 9 = ^2 & 9 x^2-6 x y +y^2=9 ^2 aligned

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