Question

Giải giúp mình với:

4a²+5-4a+b²>2b

Answer 1

ý là cm cái đó hả

Answer 2

\(4a^2+5-4a+b^2>2b\)

\(\Rightarrow4a^2+5-4a+b^2-2b>0\)

\(\Rightarrow\left(4a^2-4a+1\right)+\left(b^2-2b+1\right)+3>0\)

\(\Rightarrow\left(2a-1\right)^2+\left(b-1\right)^2+3>0\)

Dễ thấy: \(\left(2a-1\right)^2\ge0\forall a;\left(b-1\right)^2\ge0\forall b\)

\(\Rightarrow\left(2a-1\right)^2+\left(b-1\right)^2\ge0\forall a,b\)

\(\Rightarrow\left(2a-1\right)^2+\left(b-1\right)^2+3\ge3>0\forall a,b\)