Question

If $(a + b\sqrt c)^n = d + e\sqrt c$, then $(a - b\sqrt c)^n = d - e\sqrt c$

score 124 · Answer 1 · 2016-08-19 07:29:12

124

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If $(a + b\sqrt c)^n = d + e\sqrt c$, then $(a - b\sqrt c)^n = d - e\sqrt c$

Published on 19 Aug 2016 - 7:29

score 442 · Answer 2 · 2016-08-19 18:42:15

442

Views

Find $\sqrt{{3\over2}(x-1)+\sqrt{2x^2 - 7x - 4}}, x \gt 4$

Published on 19 Aug 2016 - 18:42

score 174 · Answer 3 · 2026-03-30 12:22:51

174

Views

Prove that if $a+b+c=1$ then $\sum\limits_{cyc}\frac{1}{\sqrt{a^2+b^2}}\le\frac{9\sqrt{2}}{2}$

Published on 30 Mar 2026 - 12:22

score 1.7k · Answer 4 · 2016-08-22 06:27:43

1.7k

Views

How to calculate $3^{\sqrt{2}}$ with a simple calculator?

Published on 22 Aug 2016 - 6:27

score 113 · Answer 5 · 2016-08-23 01:09:40

113

Views

Calculate $\sqrt [3] {7+5\sqrt {2}}+\sqrt [3] {7-5\sqrt {2}}$

Published on 23 Aug 2016 - 1:09

score 195 · Answer 6 · 2016-08-24 07:35:40

195

Views

How to determine that the solution to the following problem is unique?

Published on 24 Aug 2016 - 7:35

score 327 · Answer 7 · 2026-03-25 09:47:07

327

Views

A conjecture with connection to the $abc$-conjecture

Published on 25 Mar 2026 - 9:47

score 1.8k · Answer 8 · 2026-03-27 15:07:32

1.8k

Views

Find $x+y+z$ From Equations Including Radicals

Published on 27 Mar 2026 - 15:07

score 496 · Answer 9 · 2016-08-27 02:46:31

496

Views

Transforming solvable equations to the de Moivre analogues

Published on 27 Aug 2016 - 2:46

score 248 · Answer 10 · 2026-03-25 09:48:57

248

Views

Conjecture: injection from exceptional abc-triplets to natural numbers

Published on 25 Mar 2026 - 9:48

score 1k · Answer 11 · 2026-03-30 23:10:03

1k

Views

$y= | \sqrt x |$, should the graph extend to include complex numbers?

Published on 30 Mar 2026 - 23:10

score 80 · Answer 12 · 2026-03-28 19:39:50

80

Views

show that $\frac{c^2}{a}+\frac{a^2}{c}+16\sqrt{ac}\ge 9(a+c)$

Published on 28 Mar 2026 - 19:39

score 275 · Answer 13 · 2026-03-25 15:44:11

275

Views

Prove the inequality $\left(\frac1a+\frac1b+\frac1c\right)\left(\frac1{1+a}+\frac1{1+b}+\frac1{1+c}\right)\ge\frac9{1+abc}$

Published on 25 Mar 2026 - 15:44

score 5.3k · Answer 14 · 2016-08-31 22:53:20

5.3k

Views

Why must a radical be isolated before squaring both sides?

Published on 31 Aug 2016 - 22:53

score 470 · Answer 15 · 2026-03-28 22:26:59

470

Views

simplify $\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}$

Published on 28 Mar 2026 - 22:26

List Question

If $(a + b\sqrt c)^n = d + e\sqrt c$, then $(a - b\sqrt c)^n = d - e\sqrt c$

Find $\sqrt{{3\over2}(x-1)+\sqrt{2x^2 - 7x - 4}}, x \gt 4$

Prove that if $a+b+c=1$ then $\sum\limits_{cyc}\frac{1}{\sqrt{a^2+b^2}}\le\frac{9\sqrt{2}}{2}$

How to calculate $3^{\sqrt{2}}$ with a simple calculator?

Calculate $\sqrt [3] {7+5\sqrt {2}}+\sqrt [3] {7-5\sqrt {2}}$

How to determine that the solution to the following problem is unique?

A conjecture with connection to the $abc$-conjecture

Find $x+y+z$ From Equations Including Radicals

Transforming solvable equations to the de Moivre analogues

Conjecture: injection from exceptional abc-triplets to natural numbers

$y= | \sqrt x |$, should the graph extend to include complex numbers?

show that $\frac{c^2}{a}+\frac{a^2}{c}+16\sqrt{ac}\ge 9(a+c)$

Prove the inequality $\left(\frac1a+\frac1b+\frac1c\right)\left(\frac1{1+a}+\frac1{1+b}+\frac1{1+c}\right)\ge\frac9{1+abc}$

Why must a radical be isolated before squaring both sides?

simplify $\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}$

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