![](https://asakura.chiba.jp/wp-content/uploads/2022/09/3ce7665bbbd95abba89e0a1087062977.jpg)
(a+b+c)2=a2+b2+c2+2ab+2bc+2ca
に![](https://asakura.chiba.jp/wp-content/uploads/2022/09/a2c32c0fe677770e4e3d9d7954cf15f8.jpg)
を代入すると
12=13+2ab+2bc+2ca
13+2ab+2bc+2ca=1
2(ab+bc+ca)=1-13=-12
ab+bc+ca=-6(アイ答)(2点)
(a-b)2+(b−c)2+(c-a)2
=a2−2ab+b2+b2−2bc+c2+c2−2ac+a2
=2a2+2b2+2c2−2ab-2bc-2ac
=2(a2+b2+c2)-2(ab+bc+ac)
=2・13−2・(-6)=26+12=38(ウエ答)(2点)
(2)
![](https://asakura.chiba.jp/wp-content/uploads/2022/09/26de60332268e6b674c641fb76db8eae.jpg)
![](https://asakura.chiba.jp/wp-content/uploads/2022/09/33ffef10ad03260d2fb26e42c8afd9e2-1.jpg)
![](https://asakura.chiba.jp/wp-content/uploads/2022/09/bfcf717b57458397816cad35ffe61bee.jpg)