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Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$ [duplicate]
inequality
contest-math
substitution
means
karamata-inequality
Find the number of natural solutions of $5^x+7^x+11^x=6^x+8^x+9^x$
calculus
real-analysis
functions
exponential-function
karamata-inequality
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
inequality
substitution
karamata-inequality
If a,b,c are sides of a triangle, prove: $ \sqrt{a+b-c} + \sqrt{b+c-a} + \sqrt{c+a-b} \le \sqrt{a} + \sqrt{b} + \sqrt{c} $
inequality
triangles
radicals
geometric-inequalities
karamata-inequality
New bounds for convex function of 2 variables
real-analysis
inequality
jensen-inequality
karamata-inequality
Maximum of $x^3+y^3+z^3$ with $x+y+z=3$
inequality
optimization
lagrange-multiplier
maxima-minima
karamata-inequality
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