Ta có: \(\left(a-2\right)^2+1\ge0\forall a\in R\)
\(\Leftrightarrow a^2-4a+4+1\ge0\forall a\in R\)
\(\Leftrightarrow a^2+5\ge4a\forall a\in R\) (đpcm)
1a)Xét a2 + 5 - 4a =a2 - 4a + 4+1=(a - 2)2+1≥≥1 hay (a -2)2 + 1 > 0
⇒⇒Đpcm
b)Xét 3(a2 + b2 + c2) -(a + b +c)2 =3a2 + 3b2 + 3c2 - a2 - b2 - c2 - 2ab - 2ac - 2bc
=2a2 + 2b2 + 2c2 - 2ab - 2ac - 2bc
=(a - b)2 + (a - c)2 + (b - c)2≥≥0 (với mọi a,b,c)
tui ko chắc lắm