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For positive $a$, $b$, $c$ with $abc=1$, show that $\sum_{cyc}\sqrt{a^2-a+1}\geq a+b+c$
inequality
contest-math
substitution
cauchy-schwarz-inequality
mixing-variables
Proof for Cauchy-Schwarz inequality for Trace [closed]
linear-algebra
trace
cauchy-schwarz-inequality
Minimum value of $ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $ [duplicate]
inequality
optimization
maxima-minima
cauchy-schwarz-inequality
Intuition for the Cauchy-Schwarz inequality that does not rely on a geometric interpretation of vectors
linear-algebra
intuition
cauchy-schwarz-inequality
Inequality $\sum\limits_{k=1}^n \frac{1}{n+k} \le \frac{3}{4}$
sequences-and-series
inequality
fractions
harmonic-numbers
cauchy-schwarz-inequality
How to prove this inequality involving $\tanh$?
trigonometry
inequality
cauchy-schwarz-inequality
geometric-inequalities
jensen-inequality
AM-GM inequality: $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{d} + \frac{d^2}{a} \geq a + b + c + d$
inequality
contest-math
a.m.-g.m.-inequality
cauchy-schwarz-inequality
proving :$\frac{ab}{a^2+3b^2}+\frac{cb}{b^2+3c^2}+\frac{ac}{c^2+3a^2}\le\frac{3}{4}$.
inequality
substitution
a.m.-g.m.-inequality
cauchy-schwarz-inequality
sum-of-squares-method
Verfication of deduction made using the Cauchy-Schwarz inequality
inequality
proof-verification
inner-products
cauchy-schwarz-inequality
Prove that $({a\over a+b})^3+({b\over b+c})^3+ ({c\over c+a})^3\geq {3\over 8}$
inequality
cauchy-schwarz-inequality
holder-inequality
jensen-inequality
uvw
with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
inequality
cauchy-schwarz-inequality
How to find the minimum value of this function?
multivariable-calculus
inequality
optimization
cauchy-schwarz-inequality
a.m.-g.m.-inequality
How to prove that $\frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\leq\frac{3\sqrt{3}}{4}$?
trigonometry
inequality
radicals
cauchy-schwarz-inequality
muirhead-inequality
Generalization of Cauchy-Schwarz/Hölder inequality
lp-spaces
sobolev-spaces
cauchy-schwarz-inequality
holder-inequality
Inequality in cyclic order : $\sum\frac{8}{(a+b)^2+4abc}+a^2+b^2+c^2\ge\sum\frac{8}{a+3}$ [closed]
inequality
contest-math
cauchy-schwarz-inequality
holder-inequality
Hard inequality for positive numbers
inequality
cauchy-schwarz-inequality
symmetric-polynomials
uvw
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
Is the following generalization of Cauchy-Schwarz inequality true?
algebra-precalculus
inequality
proof-writing
solution-verification
cauchy-schwarz-inequality
Stronger than Nesbitt's inequality $\frac{a}{\sqrt[4]{8(b^4+c^4)}}+\frac{b}{a+c}+\frac{c}{a+b}\geq\frac{3}{2}$
inequality
contest-math
a.m.-g.m.-inequality
cauchy-schwarz-inequality
Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$
algebra-precalculus
inequality
contest-math
cauchy-schwarz-inequality
a.m.-g.m.-inequality
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