Question

已知a²-4a+1=0,求代数式(a+2)²-2（a+√2)(a-√2)的值。

RT。 弱弱的提醒下 √是根号 求高手解题。十万火急额！

Answer 1

a²-4a+1=0
a²-4a=-1

(a+2)²-2（a+√桐烂仔历培2)(a-√2)
=a²+4a+4-2(a²-2)
=a²+4a+4-2a²+4
=-a²局汪+4a+8
=-(a²-4a)+8
=1+8
=9

Answer 2

(a+2)²梁轿模-2（橡缓a+√2)(a-√2)
=a²帆仔+4a+4-2(a²-2)
= -a²+4a+8
= -(a²-4a+1)+9
=9

Answer 3

(a+2)²-2（a+√2)(a-√2)
=(a+2)²-2(a²念隐-2)
=-a²誉乱+4a+8
=-(a²仔虚厅-4a)+8
=1+8
=9;

Answer 4

a²-4a+1=0
a²含早-4a= -1
(a+2)²-2（姿老橘迹团a+√2)(a-√2)
=a²+4a+4-2a²+4
= -a²+4a+8
= -（a²-4a）+8
= -（-1）+8
=9