Search results

If \frac{1}{x} + x = A then find the below expression in terms of A x^{7}+ \frac{1}{x^{7}}

If 0<z\leq y\leq x \ \textrm{prove} \frac{x^{2}y}{z} + \frac{y^{2}z}{x} + \frac{z^{2}x}{y} \geq x^{2} + y^{2} + z^{2}

if a,b,c,d,e is some order of numbers from 1 to 5. What is the maximum possible value of S=ab+bc+cd+de+ea

\textrm{Find the minimum number of points on a complex plane such that} \textrm{for any arbitrary point on the plane at least one the distance between that arbitrary point} \textrm{to the chosen points is irrational.} \textrm{For instance, suppose the minimum number of points} \textrm{...

\textrm{Solve x} (2^{x} -4)^{3} + (4^{x} -2) ^{3} = (4^{x}+ 2^{x} -6)^{3}

\textrm{1.If} \ f(\frac{x-1}{x+1})+f(\frac{-1}{x}) + f(\frac{1+x}{1-x}) = x. \textrm{Find f(x)}

\textrm{1.If X is a set with n distinct elements.} \textrm{then prove the number of pairs (A,B) is } \ 3^{n} - 2^{n} \textrm{where} \ A \subset B \ \textrm{and} \ A,B \subseteq X \textrm{2.We call a 10 digit number interesting if all the digits are different} \textrm{and the number...

Prove the equation of a line and a circle in complex plane has a general form of : \alpha \ z\overline{z}+\beta \ z + \overline{\beta\ z}+ \gamma = 0 where \alpha,\gamma \in \mathbb{R}, \beta \in \mathbb{C} Hence, or otherwise, prove If z,z_{1},z_{2} are complex numbers which...

If alb,c are sides a triangle, then prove 3(ab+bc+ca) \leq (a+b+c)^{2} \leq 4(ab+bc+ca)

Let S_{n} = \frac{5}{9} \ \frac{14}{20} \ \frac{27}{35} \ ... \ \frac{2n^{2}-n-1}{2n^{2}+n-1} then find \lim_{n\to\infty}S_{n}

Prove for n\geq 2 tan(\alpha) \ tan(2\alpha)+ tan(2\alpha) \ tan(3\alpha)+ ...+ tan((n-1)\alpha) \ tan(n\alpha) = \frac{tan(n\alpha)}{tan(\alpha)}-n

If 0< x <\frac{\pi}{2} prove sin(x) > x - \frac{x^{3}}{4}

Suppose A= 2^{n}\underbrace{\sqrt{2-\sqrt{2+\sqrt{2+...+\sqrt{2+2cos\alpha}}}}}_{n \ times} then simplify A in terms of n and \alpha , then find lim_{n\to\infty}A

If log_{a}16 + log_{\sqrt{2}}a = 9 then find a.

Suppose P(x) is a polynomial which satisfies the following condition: P(P'(x)) = 27x^{6}-27x^{4}+6x^{2}+2. find a possible polynomial, P(x), that satisfies the above condition.

Suppose a_{1},a_{2},...,a_{n} is an arithmetic sequence.Then prove \frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+...+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}} =\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}

This is the question: let P = (1-tan^{2}\frac{a}{2})(1-tan^{2}\frac{a}{2^{2}}) (1-tan^{2}\frac{a}{2^{3}})...(1-tan^{2}\frac{a}{2^{m}}) and by simplifying P, find lim_{m\to\infty}P

HI all, This is an interesting induction question. Question: prove for every positive integer n there exist positive integers x, y ,z such that $x^{2} + y^{2} = z^{n}$