11.6

Part of II Soros Olympiad 1995 - 96 (Russia)

Problems(2)

comp. with trapezoid

Source: II Soros Olympiad 1995-96 R1 11.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

The bases of the trapezoid are equal to

a

b

. It is known that through the midpoint of one of its sides it is possible to draw a straight line dividing the trapezoid into two quadrangles, into each of which a circle can be inscribed. Find the length of the other side of this trapezoid.

geometrytrapezoid

x^3+7x^2+6x+1 = perfect cube (II Soros Olympiad 1997-98 R3 11.6)

Source:

For what natural number

x

will the value of the polynomial

x^3+7x^2+6x+1

be the cube of a natural number?

number theoryperfect cubes