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Given that _x y, _z x, _y z are in GP, x y z=64 and x^3 , y^3, z^3 are in A.P. Which one of the following is correct? x, y and z are

Options

  1. Ain AP only
  2. Bin GP only
  3. Cin both AP and GP
  4. Dneither in AP nor in GP

Correct answer

C. in both AP and GP

Step-by-step solution

Given _x y, _z x, _y z are in G.P. aligned & ( _z x )^2= ( _x y ) ( _y z ) & ( x z )^2= ( y x ) ( z y )= z x & ( x z )^3=1 & x= z x=z aligned aligned & x y z=64 & y= 64 x^2 aligned Also given x^3, y^3 and z^3 are in A.P. y^3= x^3+z^3 2 = x^3+x^3 2 aligned & y^3=x^3 y=x & x=y=z & x y z=64 & x=y=z=4 aligned Thus x, y, z are in A.P. and G.P. both.

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