设2+根号3=y则2-根号3=1/yy^(x/2)+1/y^(x/2)=4y^x-4y^(x/2)+1=0设y^(x/2)=tt^2-4t+1=0t1=2-根号3, t2=2+根号3(2+根号3)^(x/2)=2-根号3(2+根号3)^(x/2)=2+根号3所以x1= -2, x2=2
