x=根号2+1分之1,求x²+2x+2的值

x=根号2+1分之1,求x²+2x+2的值
x=根号2+1分之1,求x²+2x+2的值

x=根号2+1分之1,求x²+2x+2的值
x=1/(√2+1)=√2-1
x²+2x+2
=(x+1)²+1
=(√2-1+1)²+1
=2+1
=3

x=1/(√2+1)
=(√2-1)/[(√2+1)(√2-1)]
=√2-1
那么x²+2x+2=(√2-1)^2+√2-1+2
=2+1-2√2+√2-1+2
=4-√2

x=根号2 +1分之 1=根号2 -1
x^2+2x+2=(x+1)^2+1=3