Question

[Nguyễn Minh Nhật]

Tìm giá trị lớn nhất B=(\(\sqrt{a}\)+\(\sqrt{b}\))⁴+(\(\sqrt{a}\)+\(\sqrt{c}\))⁴+(\(\sqrt{a}\)+\(\sqrt{d}\))⁴+(\(\sqrt{b}\)+\(\sqrt{c}\))⁴+(\(\sqrt{b}\)+\(\sqrt{d}\))⁴+(\(\sqrt{c}\)+\(\sqrt{d}\))⁴ Với a,b,c,d là các số dương và a+b+c+d≤1

Answer 1

[missing you =]

\(\left(\sqrt{a}+\sqrt{b}\right)^4\le\left(\sqrt{a}+\sqrt{b}\right)^4+\left(\sqrt{a}-\sqrt{b}\right)^4=2a^2+2b^2+6ab\)

\(tt\Rightarrow B\le6\left(a^2+b^2+c^2+d^2+2ab+2ac+2ad+2bc+2bd+2cd\right)=6\left(a+b+c+d\right)^2\le6\)

\(dấu"='\Leftrightarrow a=b=c=d=\dfrac{1}{4}\)