Question

Solve the system of equations: $ \sqrt{3(x - y)^2 - 4x + 8y + 5} - \sqrt x = \sqrt{y + 1}$ and $x^2y + y^2 - 3xy - 3x + 7y + 8 = 2x\sqrt{y + 3}$.

score 73 · Answer 1 · 2019-08-21 11:41:09

Solve the system of equations: $ \sqrt{3(x - y)^2 - 4x + 8y + 5} - \sqrt x = \sqrt{y + 1}$ and $x^2y + y^2 - 3xy - 3x + 7y + 8 = 2x\sqrt{y + 3}$.

score 312 · Answer 2 · 2019-08-24 16:41:29

312

Views

If $x$ and $y$ are real numbers such that $4x^2 + y^2 = 4x - 2y + 7$, find the maximum value of $5x+6y$.

Published on 24 Aug 2019 - 16:41

score 138 · Answer 3 · 2026-03-27 07:16:55

138

Views

how to prove this inequality $\sum\frac{x}{(n-1)y+1}+\frac{1}{\sum x}\ge\frac{n+1}{n}$

Published on 27 Mar 2026 - 7:16

score 105 · Answer 4 · 2026-03-28 13:21:17

105

Views

Solve the system of equations: $ \sqrt{y^2 - 8x + 9} - \sqrt[3]{xy - 6x + 12} = 1$ and $\sqrt{2(x - y)^2 + 10x - 6y + 12} - \sqrt{y} = \sqrt{x + 2}$.

Published on 28 Mar 2026 - 13:21

score 81 · Answer 5 · 2026-03-27 15:36:07

81

Views

Find minimum of function $\frac{\left| x-12\right| }{5}+\frac{\sqrt{x^2+25}}{3}$

Published on 27 Mar 2026 - 15:36

score 80 · Answer 6 · 2019-08-28 21:57:24

80

Views

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score 936 · Answer 7 · 2026-03-25 03:19:20

936

Views

Minimum and maximum sum of squares given constraints

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score 57 · Answer 8 · 2026-02-23 01:23:34

57

Views

If the integral of a function is known, can anything be said about products of integrals of the function and its Fourier transform?

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score 72 · Answer 9 · 2026-03-26 09:42:17

72

Views

Proving the inequality $4(a^6+b^6) \ge (a+b)(a^2+b^2)(a^3+b^3)$

Published on 26 Mar 2026 - 9:42

score 91 · Answer 10 · 2019-09-05 07:01:32

91

Views

For non-negative $x$, $y$, $z$ with $x+y+z=1$, find the minimum and maximum of $\sqrt{x+1}+\sqrt{y+1}+2\sqrt{z+1}$

Published on 05 Sep 2019 - 7:01

score 390 · Answer 11 · 2019-09-08 05:42:44

390

Views

Double Summation - Cauchy-Schwarz for an Array

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score 1.4k · Answer 12 · 2026-03-25 14:35:52

1.4k

Views

Show that the 2-norm of row matrix A is equal to the 2-norm of a vector (a) consisting of the same entries

Published on 25 Mar 2026 - 14:35

score 104 · Answer 13 · 2019-09-09 15:16:07

104

Views

proof based on cauchy schwartz inequality

Published on 09 Sep 2019 - 15:16

score 97 · Answer 14 · 2026-03-25 09:29:02

97

Views

$a, b, c$ are positives such that $a + b + c = 1$. Determine the maximal value of $\sum\limits_{cyc}\frac1{a(b + c)} - \frac{a^2 + b^2 + c^2}{2abc}$.

Published on 25 Mar 2026 - 9:29

score 121 · Answer 15 · 2026-03-26 01:00:35

121

Views

Optimal coefficient in Cauchy-Schwartz inequality?

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List Question

Solve the system of equations: $ \sqrt{3(x - y)^2 - 4x + 8y + 5} - \sqrt x = \sqrt{y + 1}$ and $x^2y + y^2 - 3xy - 3x + 7y + 8 = 2x\sqrt{y + 3}$.

If $x$ and $y$ are real numbers such that $4x^2 + y^2 = 4x - 2y + 7$, find the maximum value of $5x+6y$.

how to prove this inequality $\sum\frac{x}{(n-1)y+1}+\frac{1}{\sum x}\ge\frac{n+1}{n}$

Solve the system of equations: $ \sqrt{y^2 - 8x + 9} - \sqrt[3]{xy - 6x + 12} = 1$ and $\sqrt{2(x - y)^2 + 10x - 6y + 12} - \sqrt{y} = \sqrt{x + 2}$.

Find minimum of function $\frac{\left| x-12\right| }{5}+\frac{\sqrt{x^2+25}}{3}$

Cyclic inequality with square roots and three variables

Minimum and maximum sum of squares given constraints

If the integral of a function is known, can anything be said about products of integrals of the function and its Fourier transform?

Proving the inequality $4(a^6+b^6) \ge (a+b)(a^2+b^2)(a^3+b^3)$

For non-negative $x$, $y$, $z$ with $x+y+z=1$, find the minimum and maximum of $\sqrt{x+1}+\sqrt{y+1}+2\sqrt{z+1}$

Double Summation - Cauchy-Schwarz for an Array

Show that the 2-norm of row matrix A is equal to the 2-norm of a vector (a) consisting of the same entries

proof based on cauchy schwartz inequality

$a, b, c$ are positives such that $a + b + c = 1$. Determine the maximal value of $\sum\limits_{cyc}\frac1{a(b + c)} - \frac{a^2 + b^2 + c^2}{2abc}$.

Optimal coefficient in Cauchy-Schwartz inequality?

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