ami_ba

### Questions (86)

 9 Find all odd solutions for $n$ for which $3n^2+8$ is equal to a number in base $10$ which is formed by only one digit(e.g.-$222,8888888,4,99$ etc.) 8 How to prove that $\frac{1000!}{(500!)^2}$ is not divisible by 7? 7 For positve $a$, $b$, $c$, $d$ with $a+b+c+d\leq 1$, prove that $\sqrt[4]{(1-a^4)(1-b^4)(1-c^4)(1-d^4)}\geq255\cdot a b c d .$ 7 Solving these two equations 5 Solving without using of Lagrange multipliers

### Reputation (1,140)

 +5 Eliminate $\theta$ from $\lambda\cos2\theta=\cos(\theta + \alpha) \space$ and $\space \space\lambda \sin2\theta=2\sin(\theta + \alpha)$ +5 If $\frac{\cos(\alpha -3\theta)}{\cos^3 \theta}=\frac{\sin(\alpha -3\theta)}{\sin^3 \theta}=m$ prove that $\cos\alpha=\frac{2-m^2}{m}$ +5 1993 BMO inequality problem part 1 +5 Find the range of values of $x+y+z$

 4 A coin is tossed 4 times 4 Prove that $x^2 y+ y^2 z + z^2x ≥ 2(x + y + z) − 3$ 2 Equation of a pair of straight lines through the origin and passing through the intersection of two curves 0 3 cards are dealt from a well shuffled deck.

### Tags (66)

 6 algebra-precalculus × 30 4 probability × 4 4 inequality × 14 2 geometry × 9 4 contest-math × 12 2 algebraic-curves × 2 4 a.m.-g.m.-inequality × 11 2 algebraic-geometry × 2 4 cauchy-schwarz-inequality × 11 2 coordinate-systems × 2