Solution of a depressed cubic equation

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SUMMARY

The discussion centers on solving the depressed cubic equation x³ - 2x - 5 = 0, with the confirmed real solution being x ≈ 2.0946. Participants clarify that the condition 4p³ + 27q² > 0 applies to this equation, and correct a misstatement regarding the value of x, specifically addressing an incorrect value of x = 2.4142. The conversation emphasizes the importance of accurate calculations in cubic equations.

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PainterGuy
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Hi,

I was trying to solve the equation x³-2x-5=0. I solved it online and the real solution is x≈2.0946.

The following is an excerpt from the Wikipedia article on cubic equation.

1592807371902.png


The cubic equation, x³-2x-5=0, is a depressed cubic and in this case 4p³+27q²>0. But the real root of equation comes out to be different, please see below.

1592807930198.png


The correct real solution is x≈2.0946 therefore the value x=2.4142 is not correct. Where am I going? Could you please help me?

[Moderator's note: Moved from a technical forum and thus no template.]
 
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I think you swapped p and q.
 
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Thank you.

That was really silly!

1592813200902.png
 
I'd say Prozac.
 
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archaic said:
I'd say Prozac.

It just needs a hug :frown:

I think it's because all the other equations are calling him odd
 
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