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Solving equation with sqrt

asked 2012-11-05 00:30:09 -0500

Jonas gravatar image

updated 2012-11-05 02:09:55 -0500

calc314 gravatar image


I'm trying to solve the following equation:

sage: var('a b c')
(a, b, c)
sage: a==b-sqrt(b**2-c**2/4)
a == b - sqrt(b^2 - 1/4*c^2)
sage: solve(_, b)
[b == a + sqrt(b^2 - 1/4*c^2)]

In the last line Sage doesn't solve the equation for b completely. Can you give me a hint what I'm doing wrong? Thank you!

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answered 2019-03-31 04:38:37 -0500

rel gravatar image

You could use SymPy's solver instead of Maxima, which is used by default in Sage:

sage: var('a b c')
sage: eq = (a==b-sqrt(b^2-c^2/4))
sage: solve(eq,b, algorithm='sympy')

ConditionSet(b, Eq(a - b + sqrt(4*b**2 - c**2)/2, 0), {(4*a**2 + c**2)/(8*a)})
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answered 2013-01-12 03:12:35 -0500

Majid Khonji gravatar image

ridiculous sage!!

I just try to remove the square root manually then solve. It is just a workaround I try.

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answered 2012-11-05 02:43:40 -0500

achrzesz gravatar image

Squaring equations may lead to wrong solutions but if you need the solution given in Wolframalpha you can do:

var('a b c') ; 
eq=a == b - sqrt(b^2 - 1/4*c^2) 
[b == 1/8*(4*a^2 + c^2)/a]
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Asked: 2012-11-05 00:30:09 -0500

Seen: 823 times

Last updated: Nov 05 '12