List questions from a-m-g-m-inequality

Published on 16 Apr 2026 - 14:36

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Why A.M.$\geq $ G.M. not works here. Find the minimum value of $f(x)= x^2+4x+(4/x)+(1/x^2)$ for $x>0$

Published on 16 Apr 2026 - 16:42

78

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Show that problem and that equality if fulfilled iff a=b

Published on 29 Apr 2026 - 12:51

96

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A simple Inequality?

Published on 14 Apr 2026 - 2:13

685

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British Maths Olympiad (BMO) 2006 Round 1 Question 5, alternate solution possible?

Published on 16 Apr 2026 - 19:45

61

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Proving inequalities (1)

Published on 15 Apr 2026 - 23:39

1.8k

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British Maths Olympiad (BMO) 2002 Round 1 Question 3 Proof without Cauchy-Schwarz?

Published on 16 Apr 2026 - 4:36

132

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Inequality with $abc=1$,

Published on 29 Apr 2026 - 12:44

110

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If AM-GM holds for any $2^n$ positive real numbers, show that AM-GM holds for any number of positive real numbers.

Published on 14 Apr 2026 - 8:44

163

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Suppose $a,b,c\geq 0$ and $ab+bc+ca=1$, prove that $a\sqrt{a^2+1}+b\sqrt{b^2+1}+c\sqrt{c^2+1}\geq 2$.

Published on 17 Apr 2026 - 15:20

81

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Inequality with a condition

Published on 30 Apr 2026 - 14:06

271

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A tricky algebraic inequality

Published on 10 May 2026 - 13:22

67

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Induction Using AM-GM Inequality

Published on 13 Apr 2026 - 9:04

131

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Triangles geometric inequalities

Published on 12 Apr 2026 - 16:48

488

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Prove that $3\left(\frac{x}{y} + \frac{y}{z} + \frac{z}{x}\right) \geq 2(x + y + z)\left (\frac{1}{y + z} + \frac{1}{x + z} + \frac{1}{x + y}\right)$

Published on 10 May 2026 - 12:35

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Find the smallest $C>0$ such that $xy^2z^3 \leq C(x+y+z)^6$ when $x,y,z \geq 0$

Why A.M.$\geq $ G.M. not works here. Find the minimum value of $f(x)= x^2+4x+(4/x)+(1/x^2)$ for $x>0$

Show that problem and that equality if fulfilled iff a=b

A simple Inequality?

British Maths Olympiad (BMO) 2006 Round 1 Question 5, alternate solution possible?

Proving inequalities (1)

British Maths Olympiad (BMO) 2002 Round 1 Question 3 Proof without Cauchy-Schwarz?

Inequality with $abc=1$,

If AM-GM holds for any $2^n$ positive real numbers, show that AM-GM holds for any number of positive real numbers.

Suppose $a,b,c\geq 0$ and $ab+bc+ca=1$, prove that $a\sqrt{a^2+1}+b\sqrt{b^2+1}+c\sqrt{c^2+1}\geq 2$.

Inequality with a condition

A tricky algebraic inequality

Induction Using AM-GM Inequality

Triangles geometric inequalities

Prove that $3\left(\frac{x}{y} + \frac{y}{z} + \frac{z}{x}\right) \geq 2(x + y + z)\left (\frac{1}{y + z} + \frac{1}{x + z} + \frac{1}{x + y}\right)$

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