Question

Prove $\frac{d}{\sqrt{a^2+b^2+c^2}}+\sqrt{3}\ge2\left(\sqrt{\frac{d}{a+b+c}}+\frac{\sqrt{ab+bc+ca}}{a+b+c}\right)$

score 88 · Answer 1 · 2026-04-15 22:00:45

88

Views

Prove $\frac{d}{\sqrt{a^2+b^2+c^2}}+\sqrt{3}\ge2\left(\sqrt{\frac{d}{a+b+c}}+\frac{\sqrt{ab+bc+ca}}{a+b+c}\right)$

Published on 15 Apr 2026 - 22:00

score 106 · Answer 2 · 2026-04-16 07:27:14

106

Views

Find all natural numbers $x$ and $y$ satisfying the equality $19(x^2+y^2)=221+33xy$

Published on 16 Apr 2026 - 7:27

score 80 · Answer 3 · 2026-04-11 05:46:27

80

Views

"Complementary" Fourier series

Published on 11 Apr 2026 - 5:46

score 69 · Answer 4 · 2026-04-17 02:25:14

69

Views

Is factoring primes $pq$ eqivalent to discovering $p+q$, thus binding $q$ and the search for $(p+q)$ when $(q/p) < 4$?

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score 931 · Answer 5 · 2026-04-14 22:43:51

931

Views

Solving the inequality $x^2 + 4x + 3 > 0$

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score 111 · Answer 6 · 2026-04-13 09:55:50

111

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score 252 · Answer 7 · 2026-04-17 13:11:44

252

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When does $\frac{x+\sqrt{x^2-1}}{x-\sqrt{x^2-1}}+\frac{x-\sqrt{x^2-1}}{x+\sqrt{x^2-1}}=2mx+4$ have $2$ real solutions?

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score 156 · Answer 8 · 2026-04-16 00:24:00

156

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483

Views

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70

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40

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score 331 · Answer 12 · 2026-04-15 02:37:32

331

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Finding the height of a ball modeled with $f(x) = -2(x-1)^2+7\,$?

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score 73 · Answer 13 · 2026-04-11 07:55:18

73

Views

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score 50 · Answer 14 · 2026-04-14 14:12:55

50

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score 64 · Answer 15 · 2026-04-13 18:00:17

64

Views

solving a quadratic with tensor coefficients

Published on 13 Apr 2026 - 18:00

List Question

Prove $\frac{d}{\sqrt{a^2+b^2+c^2}}+\sqrt{3}\ge2\left(\sqrt{\frac{d}{a+b+c}}+\frac{\sqrt{ab+bc+ca}}{a+b+c}\right)$

Find all natural numbers $x$ and $y$ satisfying the equality $19(x^2+y^2)=221+33xy$

"Complementary" Fourier series

Is factoring primes $pq$ eqivalent to discovering $p+q$, thus binding $q$ and the search for $(p+q)$ when $(q/p) < 4$?

Solving the inequality $x^2 + 4x + 3 > 0$

Isn't my book's solution about quadratic equations wrong?

When does $\frac{x+\sqrt{x^2-1}}{x-\sqrt{x^2-1}}+\frac{x-\sqrt{x^2-1}}{x+\sqrt{x^2-1}}=2mx+4$ have $2$ real solutions?

Solving $x^\dagger A_ix=0$ , $x^\dagger x=1$

Factoring $4x^2-2xy-4x+3y-3$. Why isn't it working?

Solve fractional inequalities that have quadratics

How much information can be gleaned from a quadratic equation?

Finding the height of a ball modeled with $f(x) = -2(x-1)^2+7\,$?

Unsure how to solve this quadratic formula problem and how to expand and substitute into the formula

Simulating an attack with a fixed number of shooters and targets, where a single random value yields the number of targets hit

solving a quadratic with tensor coefficients

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