a√a+b√b=182 then find the a,b values

x^3 +y^3 =182
if x=1 ,y not possible
if x=2,y^3=174,not possible as has to be an integer
if x=3,y^3=155,not possible as has to be an integer
if x=4,y^3=182-64=118,not possible as has to be an integer
if x=5,y^3=182-125=57,not possible as has to be an integer
thus no value of x and y will satisfy it
thus given equation will not have any solutions

Approved