21 tháng 6 2022 lúc 15:15
Cho các số thực a, b, c, d không âm thỏa mãn \(a+b+c+d=1\). Chứng minh rằng :
\(\left(\sqrt{ab+bc+cd+da}-\dfrac{1}{2}\right)^2+\left(\sqrt{ab+bc+cd+bd}-\dfrac{1}{2}\right)^2+\left(\sqrt{bc+cd+da+ac}-\dfrac{1}{2}\right)^2+\left(\sqrt{ab+cd+da+bd}-\dfrac{1}{2}\right)^2\)
\(+\left(\sqrt{ab+bc+da+ac}-\dfrac{1}{2}\right)^2+\left(\sqrt{ab}-\sqrt{ac}\right)^2+\left(\sqrt{bc}-\sqrt{bd}\right)^2+\left(\sqrt{cd}-\sqrt{ac}\right)^2+\left(\sqrt{da}-\sqrt{db}\right)^2\)
\(+\dfrac{\left(\sqrt{a}+\sqrt{b}\right)^2+\left(\sqrt{b}+\sqrt{c}\right)^2+\left(\sqrt{c}+\sqrt{d}\right)^2+\left(\sqrt{d}+\sqrt{a}\right)^2}{2}\le2\)
Gấp ạ
