Question

若x=1/根号2+1，则x²+2x+1的值=______

Answer 1

x=1/（√2+1）=√2-1
x+1=√2
x²+2x+1
=(x+1)²
=(√2)²
=2

追问

x=1/（√2+1）=√2-1 请问这步 怎么出来的。

追答

x=1/（√2+1）=(√2-1）/[(√2-1)（√2+1)]=√2-1

追问

你好，我还想问下，为什么要乘以√2-1，我比较笨 别见怪、

追答

（√2-1）（√2+1）=（√2）²-1=2-1=1
√2-1与√2+1是互为有理化因式。

Answer 2

x=（√2-1）/(√2+1)(√2-1)=√2-1
原式=(x+1)^2=2

Answer 3

x²=(1/√2+1)²=1/2+2/√2+1=3/2+2/√2
x²+2x+1=3/2+2/√2+2/√2+2+1=9/2+4/√2=（9+4√2）/2

Answer 4

x²+2x+1=（x+1）^2 =9/4 +2√2