Question

Prove that $| xy-\sqrt{(1-x^2)(1-y^2)}|\leq1$ where $|x|\leq1$ and $|y|\leq1$

score 82 · Answer 1 · 2018-08-17 19:22:04

82

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Prove that $| xy-\sqrt{(1-x^2)(1-y^2)}|\leq1$ where $|x|\leq1$ and $|y|\leq1$

Published on 17 Aug 2018 - 19:22

score 133 · Answer 2 · 2018-08-18 03:32:15

133

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AIME: I'm not sure what the question is asking for

Published on 18 Aug 2018 - 3:32

score 488 · Answer 3 · 2026-03-25 09:49:23

488

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discrete multiplicative subgroup of the reals are cyclic

Published on 25 Mar 2026 - 9:49

score 558 · Answer 4 · 2018-08-25 21:55:54

558

Views

Quadratic inequality puzzle: Prove$ |cx^2 + bx + a| ≤ 2$ given $|ax^2+bx+c| ≤ 1$

Published on 25 Aug 2018 - 21:55

score 1.6k · Answer 5 · 2026-03-25 06:10:17

1.6k

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Deciding when to drop the absolute values in differential equation?

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score 295 · Answer 6 · 2018-08-27 21:38:34

295

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How do I expand $|z_{1} - z_{2}|^2$?

Published on 27 Aug 2018 - 21:38

score 137 · Answer 7 · 2018-08-28 09:27:04

137

Views

Does $\left|\log^2{x}\right|=\log^2x$ hold true?

Published on 28 Aug 2018 - 9:27

score 12.4k · Answer 8 · 2018-08-29 03:32:37

12.4k

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Published on 29 Aug 2018 - 3:32

score 54 · Answer 9 · 2026-03-14 10:10:07

54

Views

Find $x \in \mathbb{Q}(i)$ with $ |x - 1|_{2+i} < \frac{1}{\sqrt{5}} $, $|x+1|_{2-i} < \frac{1}{\sqrt{5}}$ and $|x|_{7} < \frac{1}{7} $

Published on 14 Mar 2026 - 10:10

score 124 · Answer 10 · 2018-09-01 16:39:28

124

Views

Textbook has a strange section on absolute value that I don't quite understand

Published on 01 Sep 2018 - 16:39

score 467 · Answer 11 · 2018-09-05 15:08:14

467

Views

Explicit absolute value of $\mathbb{C}_p$ and completion of algebraic closure of $\mathbb{F}_p((t))$

Published on 05 Sep 2018 - 15:08

score 39 · Answer 12 · 2026-03-25 01:24:16

39

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score 166 · Answer 13 · 2018-09-09 19:16:10

166

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score 145 · Answer 14 · 2026-03-16 12:09:21

145

Views

Veach's thesis, projected solid angle sanity check

Published on 16 Mar 2026 - 12:09

score 4.4k · Answer 15 · 2018-09-10 23:15:07

4.4k

Views

What does it mean to have an absolute value equal an absolute value?

Published on 10 Sep 2018 - 23:15

List Question

Prove that $| xy-\sqrt{(1-x^2)(1-y^2)}|\leq1$ where $|x|\leq1$ and $|y|\leq1$

AIME: I'm not sure what the question is asking for

discrete multiplicative subgroup of the reals are cyclic

Quadratic inequality puzzle: Prove$ |cx^2 + bx + a| ≤ 2$ given $|ax^2+bx+c| ≤ 1$

Deciding when to drop the absolute values in differential equation?

How do I expand $|z_{1} - z_{2}|^2$?

Does $\left|\log^2{x}\right|=\log^2x$ hold true?

Can I Multiply Absolute Value Expressions

Find $x \in \mathbb{Q}(i)$ with $ |x - 1|_{2+i} < \frac{1}{\sqrt{5}} $, $|x+1|_{2-i} < \frac{1}{\sqrt{5}}$ and $|x|_{7} < \frac{1}{7} $

Textbook has a strange section on absolute value that I don't quite understand

Explicit absolute value of $\mathbb{C}_p$ and completion of algebraic closure of $\mathbb{F}_p((t))$

Doubt on piecewise function

Absolute value of a negative number

Veach's thesis, projected solid angle sanity check

What does it mean to have an absolute value equal an absolute value?

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