Răspuns:
(a+2)(b+3)(c+6) ≥48
Explicație pas cu pas:
Folosim inegalitatea Ma>Mg; (x+y)/2 ≥√(xy).
(a+2)/2≥√(2a)
(b+3)/2 ≥√(3b)
(c+6)/2 ≥√(6c) (×)
(a+2)(b+3)(c+6)/8 ≥√(2a)×√(3b)×√(6c) /×8
(a+2)(b+3)(c+6) ≥8√(36×abc); abc=1
=>(a+2)(b+3)(c+6) ≥8×6
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Verified answer
Răspuns:
(a+2)(b+3)(c+6) ≥48
Explicație pas cu pas:
Folosim inegalitatea Ma>Mg; (x+y)/2 ≥√(xy).
(a+2)/2≥√(2a)
(b+3)/2 ≥√(3b)
(c+6)/2 ≥√(6c) (×)
(a+2)(b+3)(c+6)/8 ≥√(2a)×√(3b)×√(6c) /×8
(a+2)(b+3)(c+6) ≥8√(36×abc); abc=1
=>(a+2)(b+3)(c+6) ≥8×6
(a+2)(b+3)(c+6) ≥48