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Stas B.

Guest

Simplifying an Expression

2/3*19^(1/2)*cos(1/3*arccos(7/38*19^(1/2))) - 1/3
Could anyone please help me simplifying this?

Thanks in advance,
Stas B.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Simplifying an Expression

If any one could solve

manually,
I will get you a satisfactory answer.

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X'(y-Xβ)=0

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Simplifying an Expression

2.507018644 using a TI-36X Solar calculator
Same answer in radians or degrees, which makes sense if you think about it.

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igloo myrtilles fourmis

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Simplifying an Expression

Stas B.: Using this bracketing: (((2/3)*(19^(1/2)))*(cos(((1/3)*(acos(((7/38)*(19^(1/2)))))))))-(1/3), Answer = 2.50701864409298

George, Graphically not Manually:   Plot of 4*x^3-3*x-7/(2*sqrt(19))

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Simplifying an Expression

Thanks, MIF. From your graph, I get positive solution  about 1.  And treat√19 = 4.5
Use these approximations, I get an answer 2+2/3.
m is the cosine.

Last edited by George,Y (2006-06-11 18:06:13)

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X'(y-Xβ)=0

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Simplifying an Expression

As they say: "there are many ways to skin a cat"

(The function plotter is useful, even though it does seem like cheating.)

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Stas B.

Guest

Re: Simplifying an Expression

I need an exact expression of the answear.
Like mine, only simpler.

Stas B.

Guest

Re: Simplifying an Expression

Oh and George, if you were planning to find out the answear by solving that cubic aquation, that wouldn't work.
You would have to use the Cardano formula and get the cosine and arc-cosine back.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Simplifying an Expression

2/3*19^(1/2)*m-1/3

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X'(y-Xβ)=0

Stas B.

Guest

Re: Simplifying an Expression

Oh, now I see!
Thanks!
But are you sure your cubic equation is correct?

Stas B.

Guest

Re: Simplifying an Expression

It's useless.
Finding 'm' using that qubic equation doesn't give us anything because again we get the cosine and the arc-cosine I need to get rid of.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Simplifying an Expression

Unless you know another way to solve a cubic equation.

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X'(y-Xβ)=0

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Simplifying an Expression

For the cubic equation, I don't think it will help, but here are the exact answers ( I bet you didn't thought this ):

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IPBLE:  Increasing Performance By Lowering Expectations.

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Simplifying an Expression

For the cubic equation, I don't think it will help, but here are the exact answers ( I bet you didn't thought this ):

m=-\sqrt{\frac{1}{2}-\frac{1}{8} \sqrt[3]{\frac{1}{38} \left(11+21 i \sqrt{3}\right)}-\frac{1}{8} i \sqrt{3} \sqrt[3]{\frac{1}{38} \left(11+21 i
   \sqrt{3}\right)}-\frac{1}{4 2^{2/3} \sqrt[3]{\frac{1}{19} \left(11+21 i \sqrt{3}\right)}}+\frac{i \sqrt{3}}{4 2^{2/3} \sqrt[3]{\frac{1}{19} \left(11+21 i
   \sqrt{3}\right)}}}\lor m=-\sqrt{\frac{1}{2}-\frac{1}{8} \sqrt[3]{\frac{1}{38} \left(11+21 i \sqrt{3}\right)}+\frac{1}{8} i \sqrt{3} \sqrt[3]{\frac{1}{38}
   \left(11+21 i \sqrt{3}\right)}-\frac{1}{4 2^{2/3} \sqrt[3]{\frac{1}{19} \left(11+21 i \sqrt{3}\right)}}-\frac{i \sqrt{3}}{4 2^{2/3} \sqrt[3]{\frac{1}{19}
   \left(11+21 i \sqrt{3}\right)}}}\lor m=\sqrt{\frac{1}{2}+\frac{1}{4} \sqrt[3]{\frac{1}{38} \left(11+21 i \sqrt{3}\right)}+\frac{1}{2 2^{2/3} \sqrt[3]{\frac{1}{19}
   \left(11+21 i \sqrt{3}\right)}}}

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IPBLE:  Increasing Performance By Lowering Expectations.