Problem 1 Transform the equation ab2(1(a+c)2+1(a−c)2)=(a−b)ab^2 \left(\frac{1}{(a + c)^2} +\frac{1}{(a- c)^2} \right) = (a -b)ab2((a+c)21+(a−c)21)=(a−b) into a simpler form, given that a>c≥0a > c \ge 0a>c≥0 , b>0b > 0b>0 .
Problem 2 Prove or disprove: given any quadrilateral inscribed in a convex polygon, we can find a rhombus inscribed in the polygon with side not less than the shortest side of the quadrilateral.
Problem 3 Let x0=5 , xn+1=xn+1xn.x_0 = 5\, , \, x_{n+1} = x_n +\frac{1}{x_n}.x0=5,xn+1=xn+xn1. Prove that 45<x1000<45.145 < x_{1000} < 45.145<x1000<45.1 .