Question

快来看看已知：X=根号2 - 1,问：x^2+(1/x)^2,x^2-(1/x)^2 的值,谁的过程最详细分给谁,.是根

Answer 1

原题即：x=√2-1,求：x^2+1/x^2、x^2-1/x^2的值.

1/x=1/(√2-1)=(√2+1)/[(√2+1)(√2-1)]=√2+1,（注：分母有理化）

可得：x+1/x=2√2,x-1/x=-2,

x^2+1/x^2

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

=(2√2)^2-2

=8-2

=6

x^2-1/x^2

=(x+1/x)(x-1/x)

=2√2*(-2)

=-4√2