Question

If $x = \frac{\sqrt{111}-1}{2}$, calculate $(2x^{5} + 2x^{4} - 53x^{3} - 57x + 54)^{2004}$.

score 1.6k · Answer 1 · 2026-03-28 08:09:54

1.6k

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If $x = \frac{\sqrt{111}-1}{2}$, calculate $(2x^{5} + 2x^{4} - 53x^{3} - 57x + 54)^{2004}$.

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score 727 · Answer 2 · 2026-03-26 09:58:04

727

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408

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score 255 · Answer 4 · 2026-03-25 23:10:01

255

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score 2.1k · Answer 7 · 2019-05-19 12:18:48

2.1k

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$a$ and $b$ are solutions of $ \frac{1}{x^{2} - 10x-29} + \frac{1}{x^{2} - 10x-45} - \frac{2}{x^{2} - 10x-69} = 0 $, $a+b=?$

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score 82 · Answer 8 · 2026-03-30 08:24:55

82

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Expression for the sum $S = \sum_{i = 0}^{n - 1} {2n \choose i} \cdot x^i \cdot (1 - x)^{2n - i}$

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score 50 · Answer 9 · 2019-05-21 15:07:23

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score 56 · Answer 13 · 2026-03-30 08:24:09

56

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472

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score 93 · Answer 15 · 2019-05-25 05:24:41

93

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List Question

If $x = \frac{\sqrt{111}-1}{2}$, calculate $(2x^{5} + 2x^{4} - 53x^{3} - 57x + 54)^{2004}$.

ratio of cylinder to ratio of square prism

If $\sin(18^\circ)=\frac{a + \sqrt{b}}{c}$, then what is $a+b+c$?

Existence of a subset such the product of its elements is a perfect square

Ratio of 9th grade students to 10th grade students

How to find points on a graph from ratios

$a$ and $b$ are solutions of $ \frac{1}{x^{2} - 10x-29} + \frac{1}{x^{2} - 10x-45} - \frac{2}{x^{2} - 10x-69} = 0 $, $a+b=?$

Expression for the sum $S = \sum_{i = 0}^{n - 1} {2n \choose i} \cdot x^i \cdot (1 - x)^{2n - i}$

Satisfying an inequality involving complex numbers

To each point of $\mathbb Z^2$ is assigned a positive integer

An Extension to a problem of IMO 1986

Are 4 chapters enough to score good in IMO.

How to find this kind of relationship: $x-\frac{1}{x}=A$ and $x+\frac{1}{x}=\sqrt{A^2+4}$?

Proving numerator of sum is divisible by prime p

A graph with n points satisfies some conditions.

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