Yes, it is the same but there is no reason to convert to decimal. You should avoid unnecessary simplifications. The way it is done in post #5 is fine.

Ronald

2012-10-26 23:12:28

Wait a minute,1/2(sqrt(5)-1) and sqrt(1.25)-.5 is same!

bobbym

2012-10-26 22:05:51

Please check your work I am not getting that. For one root I am getting.

That is what you wanted to show.

Ronald

2012-10-26 21:56:47

Sorry it is (sqrt(sqrt(1.25)-.5))

Ronald

2012-10-26 21:55:21

I get acos(sqrt(sqrt(1.25)-1)),so?

bobbym

2012-10-26 21:02:56

Hi Ronald;

You make the substitution y = cos(x) and then solve.

Another substitution, u=y^2.

Now it is easy.

Ronald

2012-10-26 20:54:41

During class I faced a problem- cos^4(x)+cos^2(x)=1,my friend told me that x=acos(sqrt(phi-1)).when I checked it using calculator,it was correct.how is phi involved in this,please explain.