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AP EAMCET201923 Apr 2019Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If (x+ 1 x =2 ) and (y+ 1 y =2 ), then (x^3 y^3+ 1 x^3 y^3 = )

Options

  1. A(2 3( - ) )
  2. B(2 3( + ) )
  3. C(2 3( - ) )
  4. D(2 3( + ) )

Correct answer

C. (2 3( - ) )

Step-by-step solution

It is given that ( array l x+ 1 x =2 x= +i = ( 2 - ) +i ( 2 - ) x=e^ i ( 2 - ) array ) and (y+ 1 y =2 y= +i =e^ i ) Now, (x^3 y^3=e^ i ( 3 2 -3 ) e^ i 3 =e^ i ( 3 2 +(3 -3 ) ) ) ( aligned & = ( 3 2 +3 -3 )+i ( 3 2 +3 -3 ) & = (3 -3 )-i (3 -3 ) aligned ) and ( 1 x^3 y^3 = (3 -3 )+i (3 -3 ) ) So, (x^3 y^3+ 1 x^3 y^3 =2 (3 -3 )=2 3( - ) ) Hence, option (c) is correct.

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