Question

55°+x+y+z= 360° value of xyz​

Answer 1

Answer:

set f(x,y)=xy(360-x-y)=360xy-yx²-y²x=-(y)x²+(360y-y²)x

df/dx=-2xy+360y-y²=y(360-y-2x)=0→【for maximum df/dx=df/dy=0】

2x+y=360...(i)

BECAUSE f(x,y) is SYMMETRICAL IN (x,y)→

2y+x=360 【when df/dy=0】

4x+2y=720=2*360

3x=360

x=120...(i)→240+y=360→y=120

∵ x+y+z=360→z=120=y=x

② But what's the hacks all that for ?

If x+y+z=3k→

xyz=maximum , when x=y=z=k, by AM≤GM ,if x,y,z are positive.

【(x+y+z)/3 ≤ ³√(xyz)】

Step-by-step explanation:

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