Find all x ∈ R that solve this equation: x^4+x^2-x-1=1-x-x^2-x^4

Determine the numerical value of the following expression without the use of a calculator: (√2+(3^2 )^(1/4)+∑_(m=1)^3▒(1/m!-√m) ).(2^log_2⁡8 +1/2^3 -∏_(k=1)^8▒(1+1/k) )

Prove that n^5 − n is divisible by 5 for all positive integers n.

The drawing below shows two squares with side lengths a. One of the squares is rotated by 45◦ and placed in the centre of the second square. Find the surface area of the rotated square not overlapping the non-rotated square (grey area).