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AP EAMCET202318 May 2023Evening ShiftMathematicsComplex NumberActual

If 1, , ^2 are the cube roots of unity and (x+y)(x + .y ^2 ) (x ^2+y )=f(x, y) , then f(2,3)=

Options

  1. A16
  2. B24
  3. C35
  4. D45

Correct answer

C. 35

Step-by-step solution

aligned & Since, f(x, y)=(x+y) (x +y ^2 ) (x ^2+y ) & f(2,3)=(2+3) (2 +3 ^2 ) (2 ^2+3 ) & =5 (4 ^3+6 ^2+6 ^4+9 ^3 ) & =5 (4+6 ^2+6 +9 ) & =5 (13+6 ( ^2+ ) )=5(13+6 (-1)) [ ^3=1 ] & =5 7=35 aligned

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