Question

Solve for all $x $ such that $16\sin^{3}x -14\cos^{3}x = \sqrt[3]{\sin x\cos^{8}x + 7\cos^{9}x}$

score 74 · Answer 1 · 2024-03-31 12:48:46

74

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Solve for all $x $ such that $16\sin^{3}x -14\cos^{3}x = \sqrt[3]{\sin x\cos^{8}x + 7\cos^{9}x}$

Published on 31 Mar 2024 - 12:48

score 325 · Answer 2 · 2026-03-25 12:28:22

325

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Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$

Published on 25 Mar 2026 - 12:28

score 3.3k · Answer 3 · 2015-01-09 11:25:36

3.3k

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Show that $\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8} = 1$

Published on 09 Jan 2015 - 11:25

score 316 · Answer 4 · 2015-01-10 17:50:24

316

Views

Find the square root of a term with a variable

Published on 10 Jan 2015 - 17:50

score 563 · Answer 5 · 2015-01-10 19:27:52

563

Views

How to Simplify Fractions with Radicals

Published on 10 Jan 2015 - 19:27

score 72 · Answer 6 · 2026-03-26 13:00:52

72

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Is there a systematic method of knowing if $n = \sqrt a $ is or is not a rational number?

Published on 26 Mar 2026 - 13:00

score 85 · Answer 7 · 2015-01-13 15:54:32

85

Views

Simplify the following Radical

Published on 13 Jan 2015 - 15:54

score 23 · Answer 8 · 2015-01-14 20:16:05

23

Views

How get variable values when one of them is within non-trivial radical

Published on 14 Jan 2015 - 20:16

score 160 · Answer 9 · 2015-01-15 07:37:50

160

Views

Basic exercise with exponents and radicals

Published on 15 Jan 2015 - 7:37

score 1.1k · Answer 10 · 2026-03-26 07:59:22

1.1k

Views

Is this attempt of showing the square root of two is irrational valid?

Published on 26 Mar 2026 - 7:59

score 4.7k · Answer 11 · 2026-03-29 19:10:54

4.7k

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How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$?

Published on 29 Mar 2026 - 19:10

score 143 · Answer 12 · 2015-01-20 20:56:30

143

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Find the limit $\sqrt[3]{n^3+n^2} - \sqrt[3]{n^3+1}$

Published on 20 Jan 2015 - 20:56

score 345 · Answer 13 · 2015-01-20 20:56:36

345

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How to prove this limit: $\lim\limits_{n \to \infty} \frac1{\sqrt[n] n}=1 $?

Published on 20 Jan 2015 - 20:56

score 126 · Answer 14 · 2015-01-20 21:12:57

126

Views

Solve for $y$ in $x=\sqrt{(y-1)/(y+1)}$

Published on 20 Jan 2015 - 21:12

score 392 · Answer 15 · 2026-04-01 19:16:02

392

Views

Why is $\frac{\sqrt{x+1}-1}{x}$ equal to $\frac{1}{\sqrt{x+1}+1}$?

Published on 01 Apr 2026 - 19:16

List Question

Solve for all $x $ such that $16\sin^{3}x -14\cos^{3}x = \sqrt[3]{\sin x\cos^{8}x + 7\cos^{9}x}$

Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$

Show that $\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8} = 1$

Find the square root of a term with a variable

How to Simplify Fractions with Radicals

Is there a systematic method of knowing if $n = \sqrt a $ is or is not a rational number?

Simplify the following Radical

How get variable values when one of them is within non-trivial radical

Basic exercise with exponents and radicals

Is this attempt of showing the square root of two is irrational valid?

How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$?

Find the limit $\sqrt[3]{n^3+n^2} - \sqrt[3]{n^3+1}$

How to prove this limit: $\lim\limits_{n \to \infty} \frac1{\sqrt[n] n}=1 $?

Solve for $y$ in $x=\sqrt{(y-1)/(y+1)}$

Why is $\frac{\sqrt{x+1}-1}{x}$ equal to $\frac{1}{\sqrt{x+1}+1}$?

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