User user350331

12 votes

3 answers

1k views

How to solve this determinant equation in a simpler way

asked Aug 12, 2016 at 5:06

10 votes

0 answers

179 views

Solve $\frac{1}{\left\lfloor{x}\right\rfloor}+\frac{1}{\left\lfloor{2x}\right\rfloor}=\{x\}+\frac13$ [duplicate]

algebra-precalculus ceiling-and-floor-functions fractional-part

asked Nov 18, 2016 at 17:26

9 votes

2 answers

7k views

Number of $5$-digit numbers which are divisible by $11$ and whose digits add up to $43$

combinatorics elementary-number-theory

asked Mar 17, 2017 at 17:47

8 votes

3 answers

241 views

To prove the inequality:- $\frac{4^m}{2\sqrt{m}}\le\binom{2m}{m}\le\frac{4^m}{\sqrt{2m+1}}$

algebra-precalculus inequality binomial-coefficients

asked Dec 25, 2016 at 6:59

8 votes

6 answers

695 views

A better way to evaluate a certain determinant

determinant

asked Oct 15, 2016 at 8:57

7 votes

3 answers

765 views

Real roots of $z^2+\alpha z + \beta=0$

complex-numbers quadratics

asked Jul 9, 2016 at 17:01

6 votes

2 answers

9k views

Forming seven letter words by using the letters of the word $\text{SUCCESS}$

combinatorics proof-verification permutations

asked Dec 29, 2016 at 8:12

6 votes

2 answers

451 views

How to solve this determinant

linear-algebra determinant

asked Aug 12, 2016 at 4:25

5 votes

2 answers

16k views

Solve the equation $x^2+\frac{9x^2}{(x+3)^2}=27$

algebra-precalculus quadratics

asked Nov 18, 2016 at 16:24

5 votes

1 answer

179 views

An inequality involving two complex numbers

algebra-precalculus inequality complex-numbers

asked Jul 15, 2016 at 13:24

5 votes

1 answer

610 views

Circles in complex plane.

complex-analysis inequality complex-numbers

asked Jul 22, 2016 at 16:54

5 votes

2 answers

154 views

Find the value of $\sum_{r=0}^{\left\lfloor\frac{n-1}3\right\rfloor}\binom{n}{3r+1}$

complex-analysis binomial-theorem

asked Jul 24, 2016 at 15:46

5 votes

3 answers

585 views

Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$

roots quadratics

asked Nov 12, 2016 at 16:20

4 votes

2 answers

101 views

Condition for the roots of $x^n+a_1x^{n-1}+a_2x^{n-2}+\ldots+a_n=0$ not all to be real

algebra-precalculus polynomials roots

asked Nov 14, 2016 at 9:38

4 votes

1 answer

307 views

Determinant with integrals

integration determinant

asked Oct 27, 2016 at 6:23

4 votes

1 answer

3k views

Write the given Determinant as the product of two Determinants

determinant

asked Nov 3, 2016 at 12:50

4 votes

3 answers

281 views

Prove that $\left|\frac{z_1-z_2}{1-z_1\bar{z_2}}\right|\lt 1$ [duplicate]

complex-analysis algebra-precalculus inequality complex-numbers complex-geometry

asked Jul 10, 2016 at 12:17

4 votes

2 answers

8k views

Jacobian of implicit functions

multivariable-calculus jacobian implicit-function

asked Oct 1, 2017 at 16:54

4 votes

2 answers

279 views

What is wrong with this false proof of $\pi=0$?

integration fake-proofs

asked Apr 15, 2019 at 13:04

3 votes

4 answers

117 views

How to find in a more formal way $\lfloor{(2+\sqrt3)^4}\rfloor$

algebra-precalculus binomial-theorem

asked Apr 27, 2017 at 14:36

3 votes

2 answers

351 views

Product of the digits of an integer $n$

number-theory solution-verification

asked May 18, 2017 at 18:28

3 votes

3 answers

432 views

What are the trailing number of the zeroes in the given integer

elementary-number-theory summation factorial decimal-expansion

asked Mar 8, 2017 at 11:03

3 votes

5 answers

2k views

Prove:$x^2+2xy+3y^2-6x-2y\ge-11\;\;\forall(x,y)\in\Bbb{R}$

inequality quadratics

asked Nov 26, 2016 at 16:34

3 votes

0 answers

1k views

Distinct roots of the equation $ax^2-bx+c=0$ in $(1,2)$, where $a,b,c\in\Bbb{N}$

elementary-number-theory roots quadratics

asked Nov 17, 2016 at 2:54

3 votes

2 answers

75 views

To prove the given inequality

sequences-and-series inequality alternative-proof

asked Jun 30, 2016 at 13:35

3 votes

2 answers

211 views

On real part of the complex number $(1+i)z^2$

complex-analysis inequality complex-numbers

asked Jul 23, 2016 at 5:18

3 votes

1 answer

140 views

How to evaluate the given determinant

determinant

asked Oct 15, 2016 at 12:04

3 votes

2 answers

150 views

Prove that the given determinant is not zero

systems-of-equations determinant

asked Oct 28, 2016 at 11:29

3 votes

2 answers

13k views

Condition for exactly one root being common b/w two quadratic equations

quadratics

asked Nov 8, 2016 at 14:46

3 votes

1 answer

169 views

Quadratic Equation in $x$ and $y$

algebra-precalculus roots quadratics

asked Nov 15, 2016 at 14:36

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71 Questions

How to solve this determinant equation in a simpler way

Solve $\frac{1}{\left\lfloor{x}\right\rfloor}+\frac{1}{\left\lfloor{2x}\right\rfloor}=\{x\}+\frac13$ [duplicate]

Number of $5$-digit numbers which are divisible by $11$ and whose digits add up to $43$

To prove the inequality:- $\frac{4^m}{2\sqrt{m}}\le\binom{2m}{m}\le\frac{4^m}{\sqrt{2m+1}}$

A better way to evaluate a certain determinant

Real roots of $z^2+\alpha z + \beta=0$

Forming seven letter words by using the letters of the word $\text{SUCCESS}$

How to solve this determinant

Solve the equation $x^2+\frac{9x^2}{(x+3)^2}=27$

An inequality involving two complex numbers

Circles in complex plane.

Find the value of $\sum_{r=0}^{\left\lfloor\frac{n-1}3\right\rfloor}\binom{n}{3r+1}$

Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$

Condition for the roots of $x^n+a_1x^{n-1}+a_2x^{n-2}+\ldots+a_n=0$ not all to be real

Determinant with integrals

Write the given Determinant as the product of two Determinants

Prove that $\left|\frac{z_1-z_2}{1-z_1\bar{z_2}}\right|\lt 1$ [duplicate]

Jacobian of implicit functions

What is wrong with this false proof of $\pi=0$?

How to find in a more formal way $\lfloor{(2+\sqrt3)^4}\rfloor$

Product of the digits of an integer $n$

What are the trailing number of the zeroes in the given integer

Prove:$x^2+2xy+3y^2-6x-2y\ge-11\;\;\forall(x,y)\in\Bbb{R}$

Distinct roots of the equation $ax^2-bx+c=0$ in $(1,2)$, where $a,b,c\in\Bbb{N}$

To prove the given inequality

On real part of the complex number $(1+i)z^2$

How to evaluate the given determinant

Prove that the given determinant is not zero

Condition for exactly one root being common b/w two quadratic equations

Quadratic Equation in $x$ and $y$