# Nesbit

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 5 How to establish this inequality: $(1-a)(1-b)(1-c) \geq 8abc$ for $a+b+c=1$? 3 What is the most elementary proof of these inequalities? 2 Finding closed form for $1^3+3^3+5^3+…+n^3$ 2 prove that $\sqrt{4-a^2}+\sqrt{4-b^2}+\sqrt{4-c^2}+(\sqrt{3}-1)(|a-1|+|b-1|+|c-1|)\ge 3\sqrt{3}$ if $a+b+c=3$ 2 How prove this $2(x^4+y^4+z^4)+2xyz+7\ge 5(x^2+y^2+z^2)$

# 524 Reputation

 +10 How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$ +10 How prove this $2(x^4+y^4+z^4)+2xyz+7\ge 5(x^2+y^2+z^2)$ +10 What is the most elementary proof of these inequalities? +5 How to compute the induced matrix norm $\| \cdot \|_{2,\infty}$

# 10 Questions

 5 Very hard inequality: $\frac{a}{\sqrt{a+pb}}+\frac{b}{\sqrt{b+pc}}+\frac{c}{\sqrt{c+pa}} \le k_p \sqrt{a+b+c}.$ 3 Computing the norm of a linear operator 2 How to compute the induced matrix norm $\| \cdot \|_{2,\infty}$ 2 Solve: $\sum_{i=1}^n \max\left\{x-a_i,0 \right\}=1.$ 2 Linear equation: $(A^\top A+B^\top B + D)x=c$ where $A,B$ are structured sparse and $D$ is diagonal.

# 30 Tags

 14 inequality × 10 2 calculus × 3 8 arithmetic × 2 2 algebra-precalculus × 3 8 average × 2 2 sequences-and-series 8 elementary-number-theory × 2 1 real-analysis × 3 3 induction 1 optimization × 3

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 Mathematics 524 rep 28 Ask Ubuntu 242 rep 128 Stack Overflow 214 rep 19 TeX - LaTeX 194 rep 6 Area 51 156 rep 2