Question

Tính A= \(a^2+b^2+c^2-ab-bc-ca\) 

với \(\left\{{}\begin{matrix}a-b=\sqrt{2}+1\\b-c=\sqrt{2}-1\end{matrix}\right.\)

Answer 1

Ta có \(A=a^2+b^2+c^2-ab-bc-ca\Rightarrow2A=\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2\)

Lại có \(\left\{{}\begin{matrix}a-b=\sqrt{2}+1\\b-c=\sqrt{2}-1\end{matrix}\right.\Rightarrow a-c=2\sqrt{2}\)

Thay vào, ta có \(2A=\left(\sqrt{2}+1\right)^2+\left(\sqrt{2}-1\right)^2+\left(2\sqrt{2}\right)^2=14\Rightarrow A=7\)