Question

Solving $ \frac{x^2}{x-1} + \sqrt{x-1} +\frac{\sqrt{x-1}}{x^2} = \frac{x-1}{x^2} + \frac{1}{\sqrt{x-1}} + \frac{x^2}{\sqrt{x-1}}$

score 178 · Answer 1 · 2026-04-17 06:32:27

178

Views

Solving $ \frac{x^2}{x-1} + \sqrt{x-1} +\frac{\sqrt{x-1}}{x^2} = \frac{x-1}{x^2} + \frac{1}{\sqrt{x-1}} + \frac{x^2}{\sqrt{x-1}}$

Published on 17 Apr 2026 - 6:32

score 137 · Answer 2 · 2026-03-25 11:54:07

137

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Find all possible values of $ d_{17}$ knowing that $ (d_7)^2 + (d_{15})^2= (d_{16})^2$

Published on 25 Mar 2026 - 11:54

score 268 · Answer 3 · 2026-04-12 03:23:25

268

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score 82 · Answer 4 · 2026-04-08 23:38:29

82

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score 121 · Answer 5 · 2026-05-07 20:32:34

121

Views

Among $2n-1$ irrationals there are $x_1,\dots,x_n$ such that for rationals $a_i\ge0$ with $\sum_{i=1}^{n}a_i>0$, $\sum_{i=1}^{n}a_ix_i$ is irrational

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score 725 · Answer 6 · 2026-05-10 12:39:05

725

Views

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score 95 · Answer 7 · 2026-05-03 23:52:45

95

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score 5.7k · Answer 8 · 2026-05-02 18:28:32

5.7k

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score 73 · Answer 9 · 2026-04-16 16:46:52

73

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score 442 · Answer 10 · 2026-04-10 22:09:32

442

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510

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score 196 · Answer 12 · 2026-04-30 06:48:26

196

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score 407 · Answer 13 · 2026-04-16 06:49:20

407

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score 76 · Answer 14 · 2026-05-10 11:56:10

76

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score 42 · Answer 15 · 2026-05-10 13:08:45

42

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List Question

Solving $ \frac{x^2}{x-1} + \sqrt{x-1} +\frac{\sqrt{x-1}}{x^2} = \frac{x-1}{x^2} + \frac{1}{\sqrt{x-1}} + \frac{x^2}{\sqrt{x-1}}$

Find all possible values of $ d_{17}$ knowing that $ (d_7)^2 + (d_{15})^2= (d_{16})^2$

Find number of functions

Manipulating a functional equation

Among $2n-1$ irrationals there are $x_1,\dots,x_n$ such that for rationals $a_i\ge0$ with $\sum_{i=1}^{n}a_i>0$, $\sum_{i=1}^{n}a_ix_i$ is irrational

Find all functions $ f:\mathbb{R} \mapsto \mathbb{R} $ such that $f[x^2+f(y)] = y +[f(x)]^2$

Maximum of three variables function

Definition of Coprime

If $|a|\ge 2$,$|b|\ge 2$, $P(x)=x^4-(a+b)x^3+(ab+2) x^2-(a+b)x+1$, prove that all roots of $P(x)$ are real

Geometric proof in Waterloo Euclid Contest

Putnam 2016 Question A5 Finite Group Theory

Combinations of a Bracelet?

Number of ways to stack poker chips if two stacks that can be obtained from each other by reflection are considered to be equivalent?

Using induction to prove sum of certain number-theoretic function.

How can simplify following for $r$

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