Question

已知x=√2+1,求x^2-2x+3的值

1不在根号下，且用两种方法解答

Answer 1

第一种：直接代入
x²-2x+3
=(√2+1)²-2(√2+1)+3
=2+2√2+1-2√2-2+3
=2+1-2+3
=4

第二种：
x²-2x+3
=x²-2x+1+2
=(x-1)²+2
=(√2+1-1)²+2
=(√2)²+2
=2+2
=4

Answer 2

x^2=2+1+2*√2, x^2-2x+3=2+1+2*√2-2*√2-2+3=4