17 Solving $\cos^2 x+\cos^2 2x +\cos^2 3x=1$ 17 Constant of integration change 15 find $x$ and solve Equation $2^x + 3^x = 6^x + 6$ 14 Can someone explain me this summation? 12 Roots of the equation $(x^2+3x+4)^2+3(x^2+3x+4)+4=x$

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 +10 $f^2(x)+(f^\prime(x))^2 \geq 1$ $f(0)=1$ implies $f^\prime(t)=0$ +15 Given polynomial $P(x) = x^2 + ax + b$ and that there only exists one $c$ such that $P^2(c) = c$. Calculate the minimum value of $a + b + c$. +30 Prove that the diagonals of a regular octagon intersect at the angular points of a square. +10 $P(x)$ has integer coefficients and admits $4$ integer roots. Prove that $P(x) = 2$ does not admit integer roots.

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### Tags (128)

 58 algebra-precalculus × 8 29 elementary-number-theory × 12 53 calculus × 18 29 integration × 6 40 linear-algebra × 23 28 trigonometry × 3 36 matrices × 16 27 polynomials × 10 32 functions × 5 27 discrete-mathematics × 6

### Bookmarks (30)

 24 How to solve this algorithmic math olympiad problem? 21 Calculate $\int_{0}^{1} (x-f(x))^{2016} dx$, given $f(f(x))=x$. 11 Interesting integral: $I=\int_0^1 \int_0^1 \log\left( \cos(\pi x)^2 + \cos(\pi y)^2 \right)dxdy$ 11 How exactly does Mathematics help me becoming more intelligent (at least, in high school)? [closed] 8 Find all continuous functions over reals such that $f(x)+f(y) = f(x+y)-xy-1$ for all $x,y \in \mathbb{R}$