We need to find extremum of $$f(x,y,z) = yz$$ under the constraint $$g(x,y,z) = 2x^2 + 3y^2 + z^2 - 12xy + 14xz - 35$$
Using the technique of Lagrange Multipliers, leads to four simultaneous equations which are quite tedious to solve esp. in an exam-setup under limited duration of time.
Entirely alternate solutions and/or techniques that efficiently solves the above system of equations are welcome.