solve function does not give me value of root
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my code is simple:
syms x y a b c
a=0.5;
b=0.0092;
c=0.04;
y=x^2+1/x^3;
solve(a*x^2+b*y+c)
matlab gives:
ans =
RootOf(z^5 + (100*z^3)/1273 + 23/1273, z)[1]
RootOf(z^5 + (100*z^3)/1273 + 23/1273, z)[2]
RootOf(z^5 + (100*z^3)/1273 + 23/1273, z)[3]
RootOf(z^5 + (100*z^3)/1273 + 23/1273, z)[4]
RootOf(z^5 + (100*z^3)/1273 + 23/1273, z)[5]
BUT, when I change y to y=x^2+1
matlab gives:
ans =
-(156579^(1/2)*1i)/1273
(156579^(1/2)*1i)/1273
WHY is that? I dont see there is so much difference. hope someone could help me, THanks!!
2 个评论
Roger Stafford
2016-4-4
编辑：Walter Roberson
2016-4-4
The difference between "y=x^2+1/x^3" and "y=x^2+1" is that the first leads to a fifth degree polynomial equation and the second to a quadratic equation. We all learned how to solve quadratic equations in high school, but mathematicians have shown that "In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no general algebraic solution—that is, solution in radicals—to polynomial equations of degree five or higher with arbitrary coefficients". See
ZA niceguy
2016-4-5
采纳的回答
Star Strider
2016-4-4
Use the vpasolve function instead:
syms x y a b c
a=0.5;
b=0.0092;
c=0.04;
y=x^2+1/x^3;
x_sol = vpasolve(a*x^2+b*y+c)
x_sol =
-0.4157571755823635878339736950704
- 0.12544667013145313389016347683479 - 0.46115251800229378352756949075526i
- 0.12544667013145313389016347683479 + 0.46115251800229378352756949075526i
0.33332525792263492780715032437 - 0.28135841861289745219925388215346i
0.33332525792263492780715032437 + 0.28135841861289745219925388215346i
3 个评论
ZA niceguy
2016-4-4
Star Strider
2016-4-4
My pleasure.
It’s not that it’s too complex, it’s that analytic solutions to quintic and higher polynomials simply don’t exist. See Roger Stafford’s Comment to your original Question, with respect to the Abel–Ruffini theorem, for a comprehensive discussion.
Walter Roberson
2016-4-4
general analytic solutions do not exist. Some quintics and higher can be factored to lower order polynomials.
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