Find the maximum value of natural components of number $96$ that we can seperate such that all of them must be relatively prime number withh each other.

$ABC$ be atriangle with sides $AB=20$ , $AC=21$ and $BC=29$. Let $D$ and $E$ be points on the side $BC$ such that $BD=8$ and $EC=9$. Find the angle $\angle DAE$.

Find the solution of the equation $8x(2x^2-1)(8x^4-8x^2+1)=1$ in the interval $[0,1]$?

Find the solution of the functional equation $P(x)+P(1-x)=1$ with power $2015$ P.S: $P(y)=y^{2015}$ is also a function with power $2015$

The largest side of the triangle $ABC$ is equal to $1$ unit. Prove that , the circles centred at $A,B$ and $C$ wit radiuses $\frac{1}{\sqrt{3}}$ can compeletely cover the triangle $ABC$.