understanding MATLAB method in long equation

this the orginal equation

and this is the equation code

fn= 1/sqrt(5) * ( ( (1+sqrt(5)) / 2 )^n - (1-sqrt(5)/2).^n )

just to understand matlab proccess, why in the first (1+sqrt(5)) part we should put () more than the second part (1-sqrt(5)/2) even though they are the same side

to be more clear I make the () bold to mention why here we should make more () the other side

fn= 1/sqrt(5) * ( ( (1+sqrt(5)) / 2 )^n - (1-sqrt(5)/2).^n )

Answer 1

[Voss]

The 1-sqrt(5) needs parentheses around it too.

[Abdullah Sultan]

you are right , thank you so much , the difference was in decemils but with your note it's 55 exactly

anyway , why we should put 2 () ?

[Voss]

(1+sqrt(5)) / 2 means: add 1 to the square root of 5 and divide the result by 2.

1+sqrt(5) / 2 means: divide the square root of 5 by 2 and add one to the result.

The parentheses are necessary to treat the whole expression 1+sqrt(5) as the numerator of a fraction in the equation.

[Abdullah Sultan]

thank you again , your explanation is very useful ,

best regards