Jan
18
comment Find the maximum value
The derivate is $$\left(1-2\,y\right)\,\left(y-y^2\right)\,\int_{0}^{y}{{{1}\over{ \sqrt{\left(y-y^2\right)^2+x^4}}}\;dx}+\sqrt{\left(y-y^2\right)^2+y^ 4}$$. I is $>0$ if $y \in (0,\frac{1}{2})$ becaus every factor is $>0$. So The integral is increasing in this interval. One can underestimate the integral and show that it is positive in the remaining interval. But there are much simpler solutions.
Jan
18
comment Find the maximum value
+1 much more simpler than using Leibniz's rule
Jan
18
comment Find the maximum value
I think you can use Leibniz's integration rule: if $$g(y)=\int^{b(y)}_{a(y)} f(x,y) dx$$ then $$g'(y)=\int_{a(y)}^{b(y)}\frac{df}{dy}(x,y)+f(b,y)b'(y)-f(a,y)a'(y)$$ to investigate the integral
Jan
17
revised Solving $x^3 + x^2 - 4 = 0$
sum sign where wrong
Jan
17
answered Solving $x^3 + x^2 - 4 = 0$
Jan
12
answered How to solve this system for real $x,y,z$
Jan
11
comment How would I solve the following trig equation?
+1 I like your answers based on groebner basis
Jan
10
comment How find this function equation $(f(x))^2-(f(y))^2=f(x+y)\cdot f(x-y)$
@Ewan Delanoy: why do you think so?
Jan
10
answered Suppose that the roots of $x^2+px+q=0$ are rational numbers and $p,q$ are integers…
Jan
8
comment Probability Exercise (Java and C++)
you are perfectly right
Jan
6
comment Factorize Polynomials
$(z^4 + z^3 + z) \equiv (z^2 + 1) *(z^2 + z +1)+1\pmod{2}$, so $h \equiv 1 \pmod{2}$
Jan
6
revised Solution of Trigonometric equations
text formatting
Jan
6
suggested suggested edit on Solution of Trigonometric equations
Jan
6
answered Transform the expression $(2a-1)(bc-1)(de-1)- (2ace-1)(b-1)(d-1)$ to
Jan
4
comment Procedure for showing a polynomial is irreducible in $\mathbb{Q[x]}$
+1 but I think $f_2(x) = (x^2+x+1)(x^3+x^2+1)$
Jan
4
revised Procedure for showing a polynomial is irreducible in $\mathbb{Q[x]}$
changed number, otherwise the argument is not valid
Jan
4
revised Procedure for showing a polynomial is irreducible in $\mathbb{Q[x]}$
typo in polynomial
Jan
4
comment Procedure for showing a polynomial is irreducible in $\mathbb{Q[x]}$
@user115654: thank you. I worked whith a cas (maxima). When I printed out the TeX string for the polynomials to paste them into this post I had already assigned values 12 and 1 to the symbols "d" and "e" (the last line in the table!). I corrected this error.
Jan
4
revised Procedure for showing a polynomial is irreducible in $\mathbb{Q[x]}$
mentioning Eisenstein's criterion
Jan
4
revised Procedure for showing a polynomial is irreducible in $\mathbb{Q[x]}$
errors in polynomial coefficients