yja + (b -c)2 +^/b + (c- a)2 +^/c + (a-b)2 > V3 ni isbotlang.
5) Agar a, b, c > 0 bo’lsa,
va
<
4^ 1 V
>3J1 + z + x" 1 + x+у2 1 + у + z" -( z + x + y )
Y1 + y + z 1 + z + x 1 + x + y 1 + y + z 1 + z + x 1 + x + y
^ s z x y
1 + y + z 1 + z + x 1 + x + y
8 + 4(a + b + c) + 2( ab + bc + ac) + abc
12 + 4(a + b + c) + (ab + bc + ac) 12 + 4(a + b + c) + (ab + bc + ac) =
8 + 4( a + b + c) + (ab + bc + ac) + 3^ a 2b2c2 + abc 12 + 4(a + b + c) +(ab + bc + ac)
Demak, S1 < 1.
masala. Ixtiyoriy musbat a7, bj (j = 1,2,...,n) sonlar uchun
Va1-an + 4K hn < ^(a1 + b1)...(an + bn) tengsizlik o’rinli ekanligini isbotlang.
V a1 a2 an J
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