Xét : \(\left(a^2+b^2+c^2+d^2\right)+\left(a+b+c+d\right)\)
\(=\left(a^2+a\right)+\left(b^2+b\right)+\left(c^2+c\right)+\left(d^2+d\right)\)
\(=a.\left(a+1\right)+b.\left(b+1\right)+c.\left(c+1\right)+d.\left(d+1\right)\)
Ta có : \(a.\left(a+1\right)\) \(\vdots\) \(2\) \(;\) \(b.\left(b+1\right)\) \(\vdots\) \(2\) \(;\) \(c.\left(c+1\right)\) \(\vdots\) \(2\) \(;\) \(d.\left(d+1\right)\) \(\vdots\) \(2\)
\(\implies\) \(\left(a^2+b^2+c^2+d^2\right)+\left(a+b+c+d\right)\) \(\vdots\) \(2\)
Mà \(a^2+b^2+c^2+d^2=2.\left(b^2+d^2\right)\) \(\vdots\) \(2\)
\(\implies\) \(a+b+c+d\) \(\vdots\) \(2\)
Mà \(a^2+b^2+c^2+d^2\) \(\geq\) \(4\) \(\implies\) \(a+b+c+d\) là hợp số \(\left(đpcm\right)\)
mấy phần bị thiếu kia cậu ghi cho tớ là chia hết cho nhé
