Question

Prove $\frac{a^2}{(a+b)^2} \geqslant \frac{4a^2-b^2-bc+7ca}{4(a+b+c)^2}$

score 100 · Answer 1 · 2020-06-18 07:55:12

100

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Prove $\frac{a^2}{(a+b)^2} \geqslant \frac{4a^2-b^2-bc+7ca}{4(a+b+c)^2}$

Published on 18 Jun 2020 - 7:55

score 218 · Answer 2 · 2020-06-19 18:56:34

218

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What is the underlying reason behind the definition of the discriminant as an expression of the roots?

Published on 19 Jun 2020 - 18:56

score 212 · Answer 3 · 2020-06-26 02:46:48

212

Views

Is there a quick (hopefully elementary) way to prove that $6b^2c^2 + 3c^2 - 36bc - 4b^4 - 4b^2 + 53=0$ has only one solution?

Published on 26 Jun 2020 - 2:46

score 474 · Answer 4 · 2020-07-05 03:09:32

474

Views

Ramification in a splitting field

Published on 05 Jul 2020 - 3:09

score 42 · Answer 5 · 2020-07-19 14:20:54

42

Views

Unsure how to prove the amount of real roots of the equation $(1+x^2)e^x = k$

Published on 19 Jul 2020 - 14:20

score 247 · Answer 6 · 2020-07-27 14:09:31

247

Views

The quadratic equations $x^2+mx-n=0$ and $x^2-mx+n=0$ have integer roots. Prove that $n$ is divisible by $6$.

Published on 27 Jul 2020 - 14:09

score 929 · Answer 7 · 2016-07-10 22:52:19

929

Views

Using discriminant to prove that there are real solutions to a quadratic

Published on 10 Jul 2016 - 22:52

score 1k · Answer 8 · 2016-07-19 09:03:54

1k

Views

Discriminant of real cyclotomic field

Published on 19 Jul 2016 - 9:03

score 1.9k · Answer 9 · 2016-09-11 12:14:00

1.9k

Views

Minimum value of $a^2 + b^2$ so that the quadratic $x^2 + ax + (b+2) = 0$ has real roots

Published on 11 Sep 2016 - 12:14

score 1.6k · Answer 10 · 2016-10-05 17:07:22

1.6k

Views

the difference between two numbers a and b is 1, and the product of the numbers is 9.

Published on 05 Oct 2016 - 17:07

score 457 · Answer 11 · 2016-10-16 23:55:10

457

Views

What is the discriminant of the equation

Published on 16 Oct 2016 - 23:55

score 563 · Answer 12 · 2016-10-23 22:52:21

563

Views

How does Neukirch's definition of the discriminant relate to the discriminant of a polynomial?

Published on 23 Oct 2016 - 22:52

score 1.1k · Answer 13 · 2016-11-14 12:27:49

1.1k

Views

Find the value of $c$ such that $h(k(x))=0$ has equal roots, where $h(x)=5x+2$ and $k(x)=cx^2-x+2$

Published on 14 Nov 2016 - 12:27

score 23 · Answer 14 · 2016-11-14 17:18:46

23

Views

Does a full-rank set of appropriate discriminant always generate an algebraic number ring?

Published on 14 Nov 2016 - 17:18

score 177 · Answer 15 · 2016-11-18 15:39:25

177

Views

Prove that the discriminant $D\equiv 0,\ 1 \pmod{4}$?

Published on 18 Nov 2016 - 15:39

List Question

Prove $\frac{a^2}{(a+b)^2} \geqslant \frac{4a^2-b^2-bc+7ca}{4(a+b+c)^2}$

What is the underlying reason behind the definition of the discriminant as an expression of the roots?

Is there a quick (hopefully elementary) way to prove that $6b^2c^2 + 3c^2 - 36bc - 4b^4 - 4b^2 + 53=0$ has only one solution?

Ramification in a splitting field

Unsure how to prove the amount of real roots of the equation $(1+x^2)e^x = k$

The quadratic equations $x^2+mx-n=0$ and $x^2-mx+n=0$ have integer roots. Prove that $n$ is divisible by $6$.

Using discriminant to prove that there are real solutions to a quadratic

Discriminant of real cyclotomic field

Minimum value of $a^2 + b^2$ so that the quadratic $x^2 + ax + (b+2) = 0$ has real roots

the difference between two numbers a and b is 1, and the product of the numbers is 9.

What is the discriminant of the equation

How does Neukirch's definition of the discriminant relate to the discriminant of a polynomial?

Find the value of $c$ such that $h(k(x))=0$ has equal roots, where $h(x)=5x+2$ and $k(x)=cx^2-x+2$

Does a full-rank set of appropriate discriminant always generate an algebraic number ring?

Prove that the discriminant $D\equiv 0,\ 1 \pmod{4}$?

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