`\text{Ta có:}` `a^4+b^4+c^4+d^4=4abcd`
`<=>a^4+b^4+c^4+d^4-4abcd=0`
`<=>(a^4-2a^2b^2+b^4)+(c^4-2c^2d^2+d^4)+(2a^2b^2+2c^2d^2-4abcd)=0`
`<=>(a^2-b^2)^2+(c^2-d^2)^2+(2a^2b^2-4abcd+2c^2d^2)=0`
`<=>(a^2-b^2)^2+(c^2-d^2)^2+2(a^2b^2-2abcd+c^2d^2)=0`
`<=>(a^2-b^2)^2+(c^2-d^2)^2+2(ab-cd)^2=0`
`\text{Do}` `(a^2-b^2)^2≥0;(c^2-d^2)^2≥0;2(ab-cd)^2≥0`
`=>a^2-b^2=0`
`\text{Mà}` `a,b>0` `=>a=b(1)`
`\text{Tương tự:}` `c=d;ab=cd(2)`
`\text{Từ}` `(1)` và `(2)`
`=>a=c=b=d`
`@-@-@-@-@-@-@-@-@-@-@-@-@`
