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Question: Why does RealDomain:-solve return an extraneous solution?

Question:Why does RealDomain:-solve return an extraneous solution?

sursumCorda 1244 Maple 2025
solve realdomain
5 hours ago
0

As we can see, RealDomain:-solve gives an incorrect solution to the following system: 

> 

restart;
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sys := `~`[diff](sqrt(2*a^2-8*a+10)+sqrt(b^2-6*b+10)+sqrt(2*a^2-2*a*b+b^2), [a, b]):
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RealDomain:-solve(`~`[`=`](sys, 0), {a, b})

{a = 5/3, b = 5/2}, {a = a, b = 2*a/(a-1)}

 (1)
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plot(eval(sys, {max(2*5^(1/2), (2*a^2-8*a+10)^(1/2)+2^(1/2)*((a^2-4*a+5)/(a-1)^2)^(1/2)+2^(1/2)*(a^2*(a^2-4*a+5)/(a-1)^2)^(1/2)), min(2*5^(1/2), (2*a^2-8*a+10)^(1/2)+2^(1/2)*((a^2-4*a+5)/(a-1)^2)^(1/2)+2^(1/2)*(a^2*(a^2-4*a+5)/(a-1)^2)^(1/2))}[-1]), a = -infinity .. infinity)

 
> 

extrema(sqrt(2*a^2-8*a+10)+sqrt(b^2-6*b+10)+sqrt(2*a^2-2*a*b+b^2), {}, {a, b})

{max(2*5^(1/2), (2*a^2-8*a+10)^(1/2)+2^(1/2)*((a^2-4*a+5)/(a-1)^2)^(1/2)+2^(1/2)*(a^2*(a^2-4*a+5)/(a-1)^2)^(1/2)), min(2*5^(1/2), (2*a^2-8*a+10)^(1/2)+2^(1/2)*((a^2-4*a+5)/(a-1)^2)^(1/2)+2^(1/2)*(a^2*(a^2-4*a+5)/(a-1)^2)^(1/2))}

 (2)

Download solve_returns_an_unsatisfiable_real_solution.mw

This appears to be a bug; is it possible to fix it? 
Text: 

sys := diff~(sqrt(2*a^2 - 8*a + 10) + sqrt(b^2 - 6*b + 10) + sqrt(2*a^2 - 2*a*b + b^2), [a, b]):
RealDomain:-solve(sys =~ 0, {a, b});
Please Wait...