1.

For x,yepsilonR with 0 lt x lt (pi)/2 such that ((sinx)^(2y))/((cosx)^((y^(2))/2))+((cosx)^(2y))/((sinx)^((y^(2))/2))=sin2x, then y is ________.

Answer»


Solution :APPLY `AMgeGm`
`((SINX)^(2y))/((cosx)^((y^(2))/2))+((cosx)^(2y))/((sinx)^((y^(2))/2))=2(sinx.cosx)^(y-(y^(2))/4)`
It follows that `sin 2x ge 2(sinx.cosx)^(y-(y^(2))/4)`
`:' sin x .COS XLT 1implies1 le y - (y^(2))/4` or `(1-(y^(2))/2)^(2) le 0`
`impliesy=2` and `sin=cosx`
So there is a unique solution `x-(pi)/4, y=2`


Discussion

No Comment Found

Related InterviewSolutions