Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series

If positive numbers x, y, z are in A.P., then the minimum value of x+y 2 y-x + y+z 2 y-z is equal to

Correct answer

Step-by-step solution

Since x, y, z are in A.P., x+z=2 y and hence aligned & x+y 2 y-x + y+z 2 y-z = x+y z + y+z x = y x + y z + x z + z x & = x z + x+z 2 z + x+z 2 x + z x =1+ 3 2 ( x z + z x ) & 1+3[ A. M. G.M.] aligned minimum value of the given expression is 4 .

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