Find maximum value of$ |z_1 -z_2 |^2 + |z_2 -z_3 |^2 + |z_3 -z_1 |^2 $ if $|z_1 | = 2, |z_2 | = 3, |z_3 | = 4 $
27062
Given complex $|z_{1}| = 2\;\;,|z_{2}| = 3\;\;, |z_{3}| = 4\;\;$ : when and what is $\max$ of $|z_{1}-z_{2}|^2+|z_{2}-z_{3}|^2+|z_{3}-z_{1}|^2$
51769
If $x,y,z\in[-1,1]$ and $1+2xyz\geq x^2+y^2+z^2$, then can we infer $1+2(xyz)^n\geq x^{2n}+y^{2n}+z^{2n}$?
121362
If $A,B>0$ and $A+B = \frac{\pi}{3},$ Then find Maximum value of $\tan A\cdot \tan B$.
77470
Find modulus of $\frac{|z_1-z_2|}{|1-(z_1)(\overline{z_2})|}$
57736
Minimum value of $\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$
22528
maximum value of $xy+yz+zx.$ given $x+2y+z=4$
48154
Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$.
67104
Find maximum divisors of a number in range
41293
Prove the inequalities $|z_1 +z_2| \geq \frac{1}{2}(|z_1|+|z_2|)|\frac {z_1} {|z_1|} +\frac {z_2} {|z_2|}|$
46883
Demand $z=x+y$ and $x^2/4 + y^2/5 + z^2/25 = 1$. What is the maximum value of $f(x,y,z) = x^2+y^2+z^2$?
21986
What is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$?
82317
Find the minimum value of $A=\frac{2-a^3}{a}+\frac{2-b^3}{b}+\frac{2-c^3}{c}$
128091
Find the range of possible values of $\sqrt{a^2+a+1}-\sqrt{a^2-a+1}$
47706
Find the value of $ \sum_{n=1}^{\infty} \frac{n^3}{3^n} $
17751
Find the greatest value of $\arg z$ achieved on a circle in $\mathbb{C}$
154223
Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$
87513
Global maximum and minimum of $f(x,y,z)=xyz$ with the constraint $x^2+2y^2+3z^2=6$ with Lagrange multipliers?