Question

Prove that the minimum values of $x^2+y^2+z^2$ is $27$ with given condition $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1$.

score 849 · Answer 1 · 2019-11-29 03:15:33

849

Views

Prove that the minimum values of $x^2+y^2+z^2$ is $27$ with given condition $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1$.

Published on 29 Nov 2019 - 3:15

score 37 · Answer 2 · 2019-11-30 15:45:05

37

Views

If $\frac f g$ is symmetric then what conclusion can we make about $f$ and $g$?

Published on 30 Nov 2019 - 15:45

score 730 · Answer 3 · 2019-12-02 12:02:52

730

Views

If $x,y,z>0.$Prove: $(x+y+z) \left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right) \geq9\sqrt[]\frac{x^2+y^2+z^2}{xy+yz+zx}$

Published on 02 Dec 2019 - 12:02

score 73 · Answer 4 · 2019-12-03 13:39:56

73

Views

Semplification using Vandermonde determinant

Published on 03 Dec 2019 - 13:39

score 176 · Answer 5 · 2026-03-25 11:04:50

176

Views

$x,y,z>0$, prove:$\frac{x}{y+z+\sqrt[4]\frac{y^4+z^4}{2}}+\frac{y}{z+x+\sqrt[4]\frac{z^4+x^4}{2}}+\frac{z}{x+y+\sqrt[4]\frac{x^4+y^4}{2}}\geq1$

Published on 25 Mar 2026 - 11:04

score 57 · Answer 6 · 2019-12-05 19:16:24

57

Views

How is this power sum equation related to the Newton-Girard identity?

Published on 05 Dec 2019 - 19:16

score 124 · Answer 7 · 2019-12-09 19:41:48

124

Views

Convexity of even power sum symmetric functions

Published on 09 Dec 2019 - 19:41

score 121 · Answer 8 · 2019-12-14 23:13:45

121

Views

$\begin{array}{|l}x^2-y^2=7 \\ x^2+xy+y^2=37\end{array}$

Published on 14 Dec 2019 - 23:13

score 106 · Answer 9 · 2019-12-16 11:20:15

106

Views

$\frac1{(a+1)^2}+ \frac1{(b+1)^2}\geq\frac 1{1+ab}$ for positive reals $a$ and $b$

Published on 16 Dec 2019 - 11:20

score 111 · Answer 10 · 2019-12-18 15:35:05

111

Views

Proving inequality $(a^2 + b^2)^3 \ge 32(a^3 + b^3)(ab - a - b)$

Published on 18 Dec 2019 - 15:35

score 196 · Answer 11 · 2026-03-25 09:43:44

196

Views

Find maximum of $C=2(x+y+z)-xy-yz-xz$

Published on 25 Mar 2026 - 9:43

score 62 · Answer 12 · 2019-12-22 14:30:17

62

Views

Find minimum value of $P = \frac{y + z}{x}$

Published on 22 Dec 2019 - 14:30

score 444 · Answer 13 · 2026-03-25 15:57:33

444

Views

Hard inequality for positive numbers

Published on 25 Mar 2026 - 15:57

score 86 · Answer 14 · 2019-12-23 21:44:18

86

Views

How to find result of system $x+y^2-4=0$ and $y+x^2-4=0$ without using the quartic formula

Published on 23 Dec 2019 - 21:44

score 70 · Answer 15 · 2019-12-24 06:59:51

70

Views

How to prove $\frac{m(r_1 + r_2 + \cdots + r_m - 1)!}{r_1! r_2! \cdots r_m!}$ is an integer?

Published on 24 Dec 2019 - 6:59

List Question

Prove that the minimum values of $x^2+y^2+z^2$ is $27$ with given condition $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1$.

If $\frac f g$ is symmetric then what conclusion can we make about $f$ and $g$?

If $x,y,z>0.$Prove: $(x+y+z) \left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right) \geq9\sqrt[]\frac{x^2+y^2+z^2}{xy+yz+zx}$

Semplification using Vandermonde determinant

$x,y,z>0$, prove:$\frac{x}{y+z+\sqrt[4]\frac{y^4+z^4}{2}}+\frac{y}{z+x+\sqrt[4]\frac{z^4+x^4}{2}}+\frac{z}{x+y+\sqrt[4]\frac{x^4+y^4}{2}}\geq1$

How is this power sum equation related to the Newton-Girard identity?

Convexity of even power sum symmetric functions

$\begin{array}{|l}x^2-y^2=7 \\ x^2+xy+y^2=37\end{array}$

$\frac1{(a+1)^2}+ \frac1{(b+1)^2}\geq\frac 1{1+ab}$ for positive reals $a$ and $b$

Proving inequality $(a^2 + b^2)^3 \ge 32(a^3 + b^3)(ab - a - b)$

Find maximum of $C=2(x+y+z)-xy-yz-xz$

Find minimum value of $P = \frac{y + z}{x}$

Hard inequality for positive numbers

How to find result of system $x+y^2-4=0$ and $y+x^2-4=0$ without using the quartic formula

How to prove $\frac{m(r_1 + r_2 + \cdots + r_m - 1)!}{r_1! r_2! \cdots r_m!}$ is an integer?

Trending Questions

Popular # Hahtags

Popular Questions