If `x_1a n dx_2` are the roots of the equation `e^2*x^(lnx)=x^3` with `x_1> x_2,` then `x_1=2x_2` (b) `x_1=x_2^2` `(c) 2x_1=x_2^2` (d) `x_1^2=x_2^3`

Explanation

`e^2x^(ln x) = x^3`

Taking log both sides,

`=>2ln e +ln x lnx = 3ln x`

`=>(ln x)^2 - 3 ln x +2 = 0`

`=>(ln x)^2 - 2 ln x-ln x +2 = 0`

`=>(ln x -2)(lnx-1) =0`

`=> (ln x -2) = 0 or (lnx-1) = 0`

`=> x = e^2 or x = e`

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