.EXAMPLES OF MAXIMA AND MINIMA. 



15. If r* = x* + y* + z*, where 



ax 9 + fy* + cz* + 2a'yz + 2b'zx + 2cxy = 1, 

 and Ix + my + nz = 0, 



find the maximum and minimum values of r~. 



Result. They are determined by the equation 



' ( a- -5 ) - 2n?6' (6 - - z J - 2?wc' ( c 2 

 V rV \ rV V P 



^'- ZV 2 - m'b"- n*c' 8 = 0. 



