Question

Proving that $a^2x^2+(b^2+a^2-c^2)x+b^2=0$ has no real roots if $a+b>c$ and $|a-b|<c$ for real $a$, $b$, $c$

score 794 · Answer 1 · 2026-04-16 21:06:16

794

Views

Proving that $a^2x^2+(b^2+a^2-c^2)x+b^2=0$ has no real roots if $a+b>c$ and $|a-b|<c$ for real $a$, $b$, $c$

Published on 16 Apr 2026 - 21:06

score 66 · Answer 2 · 2026-04-15 12:00:08

66

Views

Easier way to prove convergence of $\sum_{n=1}^{\infty} \frac{n^{\frac{1}{3}}}{n^{\frac{5}{3}} -3}$?

Published on 15 Apr 2026 - 12:00

score 79 · Answer 3 · 2026-04-13 16:43:24

79

Views

A textbook with a proof of the Rank Theorem using only Banach's Fixed Point Theorem.

Published on 13 Apr 2026 - 16:43

score 222 · Answer 4 · 2026-04-16 20:48:48

222

Views

$\dim (\ker f \cap \ker g) = n-2$

Published on 16 Apr 2026 - 20:48

score 242 · Answer 5 · 2026-04-16 06:47:49

242

Views

Showing $\tan70° = \tan20° + 2\tan50°$

Published on 16 Apr 2026 - 6:47

score 25 · Answer 6 · 2026-04-12 03:28:07

25

Views

Can a ball not containing the origin contain its negatives?

Published on 12 Apr 2026 - 3:28

score 293 · Answer 7 · 2026-04-16 04:52:37

293

Views

Geometric proof or interpretation of the triple tangent and cotangent identities

Published on 16 Apr 2026 - 4:52

score 291 · Answer 8 · 2026-04-16 00:22:52

291

Views

$PQ= \sum_{i=1}^n p_i q_i^T$

Published on 16 Apr 2026 - 0:22

score 151 · Answer 9 · 2026-04-16 09:14:29

151

Views

Is there an elementary proof that next prime number is guaranteed to be relatively nearby, that does not involve prime number theorem-related maths?

Published on 16 Apr 2026 - 9:14

score 54 · Answer 10 · 2026-04-15 22:34:27

54

Views

Prove that $f(n)\lt g(n) \text{ when } n\ge3$ and is this a valid solution?

Published on 15 Apr 2026 - 22:34

score 53 · Answer 11 · 2026-04-13 12:05:00

53

Views

What summation rule am I missing here?

Published on 13 Apr 2026 - 12:05

score 53 · Answer 12 · 2026-04-16 15:56:02

53

Views

Prove by induction if $H_n=\sum\limits_{i=1}^{n}\frac{1}{i}$ then $H_{2^n}\ge 1+\frac{n}{2}$?

Published on 16 Apr 2026 - 15:56

score 1k · Answer 13 · 2026-04-15 21:09:16

1k

Views

Find the number of subsets $A$ of $S= \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$ such that: $x\in A\wedge 2x\in S\implies 2x \in A$

Published on 15 Apr 2026 - 21:09

score 76 · Answer 14 · 2026-04-14 03:01:23

76

Views

No alternative to polar coordinates?

Published on 14 Apr 2026 - 3:01

score 264 · Answer 15 · 2026-04-16 16:58:14

264

Views

Let $a,b,c,d\in N$ and in strictly increasing order such that $b^2-bd-d^2=a^2-ac-c^2$. Prove that $ab+cd$ is not a prime.

Published on 16 Apr 2026 - 16:58

List Question

Proving that $a^2x^2+(b^2+a^2-c^2)x+b^2=0$ has no real roots if $a+b>c$ and $|a-b|<c$ for real $a$, $b$, $c$

Easier way to prove convergence of $\sum_{n=1}^{\infty} \frac{n^{\frac{1}{3}}}{n^{\frac{5}{3}} -3}$?

A textbook with a proof of the Rank Theorem using only Banach's Fixed Point Theorem.

$\dim (\ker f \cap \ker g) = n-2$

Showing $\tan70° = \tan20° + 2\tan50°$

Can a ball not containing the origin contain its negatives?

Geometric proof or interpretation of the triple tangent and cotangent identities

$PQ= \sum_{i=1}^n p_i q_i^T$

Is there an elementary proof that next prime number is guaranteed to be relatively nearby, that does not involve prime number theorem-related maths?

Prove that $f(n)\lt g(n) \text{ when } n\ge3$ and is this a valid solution?

What summation rule am I missing here?

Prove by induction if $H_n=\sum\limits_{i=1}^{n}\frac{1}{i}$ then $H_{2^n}\ge 1+\frac{n}{2}$?

Find the number of subsets $A$ of $S= \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$ such that: $x\in A\wedge 2x\in S\implies 2x \in A$

No alternative to polar coordinates?

Let $a,b,c,d\in N$ and in strictly increasing order such that $b^2-bd-d^2=a^2-ac-c^2$. Prove that $ab+cd$ is not a prime.

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