syms x
fplot(@(x)x^3-4*x^2+39*x-46)
hold on
fplot(@(x)x^3+3*x^2+4*x-3)
hold off
grid
r=roots([1,-4,39,-46])
r2=roots([1,3,4,-3])
produces a graph showing each of the two functions crossing the x axis once (and each other twice--almost tangent), and then listing roots:
r =
1.35203442644909 + 5.80238880628641i
1.35203442644909 - 5.80238880628641i
1.29593114710183 + 0i
r2 =
-1.75799011384641 + 1.65034755068945i
-1.75799011384641 - 1.65034755068945i
0.515980227692821 + 0i
the real roots being, of course, those whose imaginary component is zero.
The fractional part of a is .29593114710183.
The fractional part of b is .515980227692821, which is in fact b itself, whose square is 0.266235595369935.
So the fractional part of a is indeed larger than the square of the fractional part of b.
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Posted by Charlie
on 2023-07-06 17:41:53 |
well it is a proof if you just solve it
