Question

Consider three numbers x, y, and z that sum to 1 and also have their squares sum to 1. Find x, y, and z so that their product is a minimum.

Answer 1

given aty+z=1 y?+2? = 1 + 2 : the product is myz . 314 let frymez)=X+Y+ 2-1. . 2 g(ximiz) 2x²+y2+2 ²4 34 legrenge method. 218,4,7) 3f (Olure) + (90941449)) = (42X1, kunt = 642 44 t = 1+ 22d. for extremum put hoc = 2y = =0 x=-ża, y s orzana put in eqn ® Hot Svetore X = 3 ) dat UB: If = 25 x 23 24 = = 1 / 2 = 1 / 23 product to 3), (- + 3) ( 53 ) = xy?

If t= -0 4 18 = 1/3 14=1 a 14 =18 pooduct Exyz = (hells) Cos) niin for minimum product t- tus) mar 19 = tz czando Thank you!