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x := (sqrt(5)-2)^(1/3)+(sqrt(5)+2)^(1/3); 1 

(5^(1/2)-2)^(1/3)+(5^(1/2)+2)^(1/3) 

y := (sqrt(5)-2)^(2/3)+(sqrt(5)+2)^(2/3)+2*(sqrt(5)-2)^(1/3)*(sqrt(5)+2)^(1/3); 1 

(5^(1/2)-2)^(2/3)+(5^(1/2)+2)^(2/3)+2*(5^(1/2)-2)^(1/3)*(5^(1/2)+2)^(1/3) 

 

simplify((sqrt(5)-2)^(2/3)+(sqrt(5)+2)^(2/3)); 1 

3 

(sqrt(5)-2)*(sqrt(5)+2); 1 

(5^(1/2)-2)*(5^(1/2)+2) 

=> 5 - 4 => 1 => 3rd-root of 1 is 1 

y := (sqrt(5)-2)^(2/3)+(sqrt(5)+2)^(2/3)+2 

(5^(1/2)-2)^(2/3)+(5^(1/2)+2)^(2/3)+2 

simplify(((sqrt(5)-2)^(2/3)+(sqrt(5)+2)^(2/3))^3); 1 

27 

y := 27^(1/3)+2 

27^(1/3)+2 

simplify(y); 1 

5 

x := sqrt(y); 1 

(27^(1/3)+2)^(1/2) 

simplify(x); 1 

5^(1/2)