9.7

Part of III Soros Olympiad 1996 - 97 (Russia)

Problems(2)

min equilateral inscirbed in 90-60-30 (III Soros Olympiad 1996-97 R1 9.7)

Source:

Find the side of the smallest regular triangle that can be inscribed in a right triangle with an acute angle of

30^o

and a hypotenuse of

2

. (All vertices of the required regular triangle must be located on different sides of this right triangle.)

geometryEquilateralinscribed

4x4 non linear system (III Soros Olympiad 1996-97 R3 9.7)

Source:

Solve the system of equations:

\begin{cases} xy+zu=14 \\ xz+yu=11 \\ xu+yz=10 \\ x+y+z+u=10 \end{cases}

system of equationsalgebra