... equality holds, there is exactly one way of placing. This hap-pens, for example, when (a, b)=(5, 20) and (c, d)=(16, 19).Second remark. This problem is essentially very similar to (SL89-2).16. ... haveλ1+λ+µ1+µ+ν1+ν=SOBCSABC+SAOCSABC+SABOSABC=1.Simplifying this relation, we get1=λµ + µν + νλ +2λµν ≥ 3(λµν)2/3+2λµν,which cannot hold if λµν >18. Hence λµν ≤18, with equality if and onlyif λ = µ = ν =12. This implies that ... tan C. Using the relation x + y + z = xyz, we can reducethis inequality to(2x + y + z)(x +2y + z)(x + y +2z) ≥ 8(x + y)(y + z)(z + x).This follows from the AM–GM inequality: 2x+ y + z =(x+ y)+(x...