# Question:trick to show this expression is zero?

## Question:trick to show this expression is zero?

Maple 2023

Given

`expr:=  (x^(-(44 + 12*sqrt(69))^(1/3)/6 + 10/(3*(44 + 12*sqrt(69))^(1/3)) + 2/3)) - (x^(sqrt(69)*2^(1/3)*((11 + 3*sqrt(69))^2)^(1/3)/100 - (11*(44 + 12*sqrt(69))^(2/3))/600 - (44 + 12*sqrt(69))^(1/3)/6 + 2/3))`

could someone come with a trick to show this is zero using simplification and other methods? I know I can use is and coulditbe but I do not trust these too much due to false positives I've seen from them in some places.

Here is my attempts

```restart;

expr:=  (x^(-(44 + 12*sqrt(69))^(1/3)/6 + 10/(3*(44 + 12*sqrt(69))^(1/3)) + 2/3)) - (x^(sqrt(69)*2^(1/3)*((11 + 3*sqrt(69))^2)^(1/3)/100 - (11*(44 + 12*sqrt(69))^(2/3))/600 - (44 + 12*sqrt(69))^(1/3)/6 + 2/3));
simplify(expr);
simplify(expr,size);
simplify(expr,symbolic);
simplify(normal(expr));
simplify(normal(expr),symbolic);
simplify(expr) assuming real;
simplify(expr) assuming positive;
is(expr=0);
coulditbe(expr=0);
evalb(expr=0);
```

Gives

This is for reference, the Mathematica attempt

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