Question

When $c$ is real and in the interval $[-1,1]$, the roots $z$ of $z^2-2cz+1=0$ have $|z|=1$.

score 122 · Answer 1 · 2026-04-06 09:58:56

122

Views

When $c$ is real and in the interval $[-1,1]$, the roots $z$ of $z^2-2cz+1=0$ have $|z|=1$.

Published on 06 Apr 2026 - 9:58

score 99 · Answer 2 · 2017-08-31 19:47:08

99

Views

Why is $\sqrt[4]{4} = \sqrt{2}$

Published on 31 Aug 2017 - 19:47

score 94 · Answer 3 · 2026-04-09 17:39:24

94

Views

Real roots of Irrational equation

Published on 09 Apr 2026 - 17:39

score 934 · Answer 4 · 2026-03-31 05:21:51

934

Views

If $abcd=1$ then $a^4b+b^4c+c^4d+d^4a\geq a+b+c+d$

Published on 31 Mar 2026 - 5:21

score 75 · Answer 5 · 2026-04-12 03:38:08

75

Views

Simplifying the difference of third roots

Published on 12 Apr 2026 - 3:38

score 107 · Answer 6 · 2026-04-11 10:16:43

107

Views

Understanding $\sqrt[i]{z}$ for $z\in\mathbb{C}, z\ne0$

Published on 11 Apr 2026 - 10:16

score 717 · Answer 7 · 2026-03-30 04:00:09

717

Views

Show that $\frac{1}{\sqrt{r_3}}=\frac{1}{\sqrt{r_1}}+\frac{1}{\sqrt{r_2}}$ for three mutually tangent circles, each tangent to a common line

Published on 30 Mar 2026 - 4:00

score 9k · Answer 8 · 2017-09-05 14:16:50

9k

Views

If $x=8+3\sqrt{7},$ then what is value of $\sqrt{x} -\frac{1}{\sqrt{x}}$?

Published on 05 Sep 2017 - 14:16

score 305 · Answer 9 · 2017-09-07 16:29:07

305

Views

I am getting two answers for the fourth root of i. What am I doing wrong?

Published on 07 Sep 2017 - 16:29

score 99 · Answer 10 · 2017-09-08 02:24:29

99

Views

Is it $100$% true that $\forall n\in \mathbb{R}, \ n^2 = (-n)^2$?

Published on 08 Sep 2017 - 2:24

score 184 · Answer 11 · 2026-04-12 13:21:30

184

Views

Approximation of square root of 2 - How does this method work

Published on 12 Apr 2026 - 13:21

score 345 · Answer 12 · 2026-04-10 18:09:07

345

Views

Inequality problem involving square roots

Published on 10 Apr 2026 - 18:09

score 43 · Answer 13 · 2017-09-09 02:37:18

43

Views

Inequality involving radicals and using the factorization of x^3-y^3

Published on 09 Sep 2017 - 2:37

score 71 · Answer 14 · 2026-04-11 09:45:33

71

Views

Surds based problem

Published on 11 Apr 2026 - 9:45

score 356 · Answer 15 · 2017-09-09 14:51:35

356

Views

Why $\sqrt{x^2}$ is not equal to $\big(\sqrt{x}\big)^2$?

Published on 09 Sep 2017 - 14:51

List Question

When $c$ is real and in the interval $[-1,1]$, the roots $z$ of $z^2-2cz+1=0$ have $|z|=1$.

Why is $\sqrt[4]{4} = \sqrt{2}$

Real roots of Irrational equation

If $abcd=1$ then $a^4b+b^4c+c^4d+d^4a\geq a+b+c+d$

Simplifying the difference of third roots

Understanding $\sqrt[i]{z}$ for $z\in\mathbb{C}, z\ne0$

Show that $\frac{1}{\sqrt{r_3}}=\frac{1}{\sqrt{r_1}}+\frac{1}{\sqrt{r_2}}$ for three mutually tangent circles, each tangent to a common line

If $x=8+3\sqrt{7},$ then what is value of $\sqrt{x} -\frac{1}{\sqrt{x}}$?

I am getting two answers for the fourth root of i. What am I doing wrong?

Is it $100$% true that $\forall n\in \mathbb{R}, \ n^2 = (-n)^2$?

Approximation of square root of 2 - How does this method work

Inequality problem involving square roots

Inequality involving radicals and using the factorization of x^3-y^3

Surds based problem

Why $\sqrt{x^2}$ is not equal to $\big(\sqrt{x}\big)^2$?

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