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New posts in tangent-line-method
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
multivariable-calculus
inequality
contest-math
symmetric-functions
tangent-line-method
Proving $\left(\frac{a}{a+b+c}\right)^2+\left(\frac{b}{b+c+d}\right)^2+\left(\frac{c}{c+d+a}\right)^2+\left(\frac{d}{d+a+b}\right)^2\ge\frac{4}{9}$
inequality
holder-inequality
rearrangement-inequality
tangent-line-method
buffalo-way
Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$
real-analysis
inequality
a.m.-g.m.-inequality
cauchy-schwarz-inequality
tangent-line-method
How to prove $|\sum_{i=1}^n a_i|\le \sqrt{n} \sqrt{\sum_{i=1}^n a_i^2}$
inequality
radicals
absolute-value
cauchy-schwarz-inequality
tangent-line-method
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
inequality
radicals
lagrange-multiplier
sum-of-squares-method
tangent-line-method
Proving a three variables inequality
inequality
tangent-line-method
A inequality proposed at Zhautykov Olympiad 2008
inequality
substitution
cauchy-schwarz-inequality
tangent-line-method
Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$
inequality
proof-writing
radicals
a.m.-g.m.-inequality
tangent-line-method
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