(3x - 2y) : (2x + 3y) = 5 : 6, then one of the value of $${\left( {\frac{{\root 3 \of x + \root 3 \of y }}{{\root 3 \of x - \root 3 \of y }}} \right)^2}$$  is?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{3x - 2y}}{{2x + 3y}} = \frac{5}{6} \cr & 18x - 12y = 10x + 15y \cr & 8x = 27y \cr & \frac{x}{y} = \frac{{27}}{8} \cr & {\left( {\frac{{\root 3 \of x + \root 3 \of y }}{{\root 3 \of x - \root 3 \of y }}} \right)^2} \cr & = {\left( {\frac{{\root 3 \of {27} + \root 3 \of 8 }}{{\root 3 \of {27} - \root 3 \of 8 }}} \right)^2} \cr & = {\left( {\frac{{3 + 2}}{{3 - 2}}} \right)^2} \cr & = {\left( 5 \right)^2} \cr & = 25 \cr} $$