04/09/21 21:59:03
>402
(a^2 +b^2 +1)^2 - 2{a(b+1)}^2
= a^4 +2(a^2)(b^2 +1) +(b^2 +1)^2 -2(a^2)(b^2 +2b +1)
= a^4 -2(a^2)(2b) + (2b)^2 + (b^2 -1)^2
= (a^2-2b)^2 + (b^2 -1)^2 ≧0.
∴ a^2 +b^2 +1 ≧ √2 |a(b+1)|.
04/09/21 21:59:03
>402
(a^2 +b^2 +1)^2 - 2{a(b+1)}^2
= a^4 +2(a^2)(b^2 +1) +(b^2 +1)^2 -2(a^2)(b^2 +2b +1)
= a^4 -2(a^2)(2b) + (2b)^2 + (b^2 -1)^2
= (a^2-2b)^2 + (b^2 -1)^2 ≧0.
∴ a^2 +b^2 +1 ≧ √2 |a(b+1)|.