Đặt \(M=\sqrt{1-a^2}+\sqrt{1-b^2}\)
\(\Rightarrow M^2=\left(\sqrt{1-a^2}+\sqrt{1-b^2}\right)^2\)
\(\le\left(1+1\right)\left(1-a^2+1-b^2\right)\) (bđt Cauchy Shwarz)
\(\le2\left[2-\dfrac{\left(a+b\right)^2}{2}\right]\) (bđt Cauchy Shwarz)
\(=4\left[1-\dfrac{\left(a+b\right)^2}{4}\right]\)
\(\Rightarrow M\le2\sqrt{1-\left(\dfrac{a+b}{2}\right)^2}\)
Dấu "=" xảy ra khi a = b