已知x=1-2的平方根,y=1+2的平方根,求1/(x+y)+1/(x-y)*[(x^2-2xy+y^2)/2x]的值._数学解答

已知x=1-2的平方根,y=1+2的平方根,求1/(x+y)+1/(x-y)*[(x^2-2xy+y^2)/2x]的值.

人气：227 ℃　时间：2020-03-29 15:57:58

解答

x+y=2,x-y=2√2,x^2-2xy+y^2=(x-y)^2 所以,1/(x+y)+1/(x-y)*[(x^2-2xy+y^2)/2x]=1/2+(x-y)/2x=1/2+√2/(1-√2)=1/2-√2-2=-√2-3/2