Jan
23
revised How do I go about algebraic manipulation of polynomials with many terms?
slightly changing a formulation
Jan
23
answered How do I go about algebraic manipulation of polynomials with many terms?
Jan
21
revised How prove this equality $4064b^6+4064c^6+1452b^2c^4+8013b^4c^2+7172b^3c^3-4728b^5c-11289bc^5\ge 0$
added 38 characters in body
Jan
21
revised How prove this equality $4064b^6+4064c^6+1452b^2c^4+8013b^4c^2+7172b^3c^3-4728b^5c-11289bc^5\ge 0$
other ways I tried
Jan
21
answered How prove this equality $4064b^6+4064c^6+1452b^2c^4+8013b^4c^2+7172b^3c^3-4728b^5c-11289bc^5\ge 0$
Jan
19
comment Complex numbers modulus/argument question
It can be transformed to $$\frac{\text{Im}(z)}{1-\text{Re}(z)}i$$.
Jan
18
comment Complex numbers modulus/argument question
Yes, I now I see this. But then it is possible to simplify $|1-z|^2$ further.
Jan
18
comment Complex numbers modulus/argument question
why does the $|1-z|^2$ disappear
Jan
18
comment Calculation of the derivative of $e^{\cos(x)}$ from first principles
calculating the derivate uses the chain rule and the rules for $\cos$ and $\exp$. So you could try to mimic a proof of the chain rule.
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 $h \equiv 1 \pmod{2}$