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AP EAMCET202420 May 2024Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If + + = + + =0 then ( ^3 + ^3 + ^3 )^2+ ( ^3 + ^3 + ^3 )^2=

Options

  1. A1
  2. B3 4
  3. C9 16
  4. D9 8

Correct answer

C. 9 16

Step-by-step solution

Let x= +i , y= +i and z= +i x+y+z=0 x^3+y^3+z^3=3 x y z ( +i )^3+( +i )^3+( +i )^3=3( +i )( +i )( +i ) ( 3 + 3 + 3 )+i( 3 + 3 + 3 )=3 ( + + )+3 i ( + + ) 3 + 3 + 3 =3 ( + + ) 4 ^3 -3 +4 ^3 -3 +4 ^3 -3 =3 ( + + ) 4 ( ^3 + ^3 + ^3 )=3 ( + + ) ^3 + ^3 + ^3 = 3 4 ( + + ) Similarly, ^3 + ^3 + ^3 = -3 4 ( + + ) Now, ( ^3 + ^3 + ^3 )^2+ ( ^3 + ^3 + ^3 )^2= 9 16 ^2( + + )+ 9 16 ^2( + + )= 9 16

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