easy let cuberoot(9+sqrt(80))+ cuberoot(9-sqrt(80))=x

now cube on both l.h.s and r.h.s

apply (a+b)^(3)=a^3+b^3+3ab(a+b)

now

x^(3)=9+sqrt(80)+9-sqrt(80)+3*cuberoot(9+sqrt(80))*cuberoot(9-sqrt(80))*(x)

now (9-sqrt(80))=1/(9+sqrt(80))

therefore the two cuberoot terms would be cancelled

now

x^(3)=18-3x

x^(3)+3x-18=0

now apply factor theorem take (x-3) and divide this to the above cubic eqn

we thus get x=3 as root

substitute the value of x and u will get the result