# D3r0X4

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bio website location age 15 member for 1 year, 4 months seen 4 hours ago profile views 183

Secondary student from ... Earth

# 58 Questions

 21 Find integer in the form: $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$ 15 Find $x,y,z \in \mathbb Q$ such that $x + \frac 1y, y + \frac 1z, z+ \frac 1x \in \mathbb Z$ 13 Prove $\sum_{i=0}^n \binom{n}{i}^2x^{n-i} = 0$ has $n$ negative roots 12 Find $x\in \mathbb{Z}$ such that $54x^3+1$ is a cube 10 Find minimum of $\frac x {x^2+1} + \frac y{y^2+1} + \frac z{z^2+1}$

# 1,381 Reputation

 +2 $(x+2/(x^2+x))$$(y+2/ (y^2+y))$ product is equal to positive integers, general solution +5 Prove $\sum_{i=0}^n \binom{n}{i}^2x^{n-i} = 0$ has $n$ negative roots +10 Find all finite set S such that any $a, b, c \in S$, $ab + bc + ca \in S$ +5 Prove inequality $(x+y+z-2xyz)^2 \le 2$

 5 Factoring $n^4+4$ 5 Find maxi,minimum $f(x,y)=x^3+y^3 (\text{where} ~~~ x,y\in \mathbb{R}, x^2+y^2=1)$ 2 Prove $x^2+y^2+z^2 \ge 14$ with constraints 1 Assume $n$ is even. Prove that $323$ divides $20^n+16^n-3^n-1$. 0 Two Problem: find max, min; number theory: find x, y

# 28 Tags

 7 homework × 11 0 number-theory × 20 5 calculus 0 diophantine-equations × 11 2 inequality × 31 0 geometry × 4 2 optimization × 7 0 algebra-precalculus × 3 1 elementary-number-theory × 11 0 problem-solving × 3

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