Let $x = (a^2+a+1)^{1/2}-(a^2-a+1)^{1/2}$ and $a$ belongs to real number find all possible value of $x$.
128091
Find the range of possible values of $\sqrt{a^2+a+1}-\sqrt{a^2-a+1}$
155363
Find all integers $(x, y)$ such that $1 + 2^x + 2^{2x + 1} = y^2$
122948
$x^{x^{x^{\dots}}}=2$, what is the value of $x$?
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
156956
Give the remainder of $x^{100}$ divided by $(x-2)(x-1)$.
5868
Find the real number $x$ represented by continued fraction $[12;2,2,12,2,2,12,2,2,12\dots]$
2300
Determine the remainder when $f(x) = 3x^5 - 5x^2 + 4x + 1$ is divided by $(x-1)(x+2)$
114043
Prove the existence of a real number satisfying a property
17647
Which complex exponent can turn x into a -x?
124581
Solving $x^2 - 1 = e^x$
130149
Computablility of a real number
115719
Find the possible values of |A + B + C |
140622
Find the value of : $\lim_{x \to \infty} \sqrt{4x^2 + 4} - (2x + 2)$
112950
Find the value of infinite series $\sum_{n=1}^{\infty} \tan^{-1}(2/n^2)$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
122686
Find the root of the polynomial?
59196
Find all real solutions for $x$ in $ 2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2 . $