已知x=根号3减根号2分之根号3加根号2,y=根号3加根号2分之根号3减根号2,x²加y²加2018

更新时间2018-04-29 19:22:51

已知x=根号3减根号2分之根号3加根号2,y=根号3加根号2分之根号3减根号2,x²加y²等于多少

x=(√3+√2)/(√3-√2)

y=(√3-√2)/(√3+√2)

x+y=(√3+√2)/(√3-√2)+(√3-√2)/(√3+√2)

      =(√3+√2)^2/(√3-√2)(√3+√2)+(√3-√2)^2/(√3+√2)(√3-√2)

     =(5+2√6)/1+(5-2√6)/1

     =10

xy=(√3+√2)/(√3-√2)*(√3-√2)/(√3+√2)=1

x^2+y^2

=(x+y)^2-2xy

 =10^2-2*1

=100-2

=98