SOLUTION: if a, b belong to R+ such that {{{system(a*sqrt(a) + b*sqrt(b) = 183, a*sqrt(b) + b*sqrt(a) = 182)}}} then {{{(9/5)(a + b )= "?"}}}

System 1:      

Let , ,  , , then



System 2:     

Multiply the 2nd equation by 3



Add the two equations:



Factor the left side:
 


Take cube roots of both sides:

Eq. 1     

Factor the left side of the 1st equation in system 2




Use Eq. 1 to substitute 9 for (x+y)


, reduce 183/9 to 61/3

Eq. 2     

Square both sides of Eq. 1:



Eq. 3     

Multiply Eq. 2 by -1 and add Eq. 3


 






Substitute  for xy in in Eq. 2







Since x²=a and y²=b,





Edwin