If x, y and z are real numbers such that: x + y + z = 5 and xy + yz
+ zx = 3. What is the largest value that any of the numbers can
Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7
If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.
Published December 1999,February 1999,December 2011,February 2011.
While studying the school course of chemistry we were taught two
methods of defining the coefficients in the equations of chemical
reactions: the method of manual selection and the method of
electronic balance for the reactions of oxidation and reduction. I
was surprised by the imperfection of these methods. In the work
that is presented to your attention I suggest a simple method of
defining the coefficients in the equations of chemical reactions
with the help of a system of linear algebraic equations that
describes the material balance in a chemical reaction.