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20 12 9th grade of national mathematics league: if a~2+b~2= 1, the minimum value of a~4+ab+b~4 is
Because a-2+b-2= 1, a=5-b,

From A-4+AB+B-4 = (A-2+B-2)+AB-4 =1+AB-4.

Get b(5-b)-3=-b squared +5b-3.

The square of formula -(b-2/5) is+13/4.

So when b=2/5, the maximum value is 13/4.