已知根号X+根号x分之1=5,求x平方+x+1分之x-x+1分之x的值

根号X+1/根号x=5,两边平方得：x+1/x+2=25x+1/x=23x^2+1/x^2+2=529x^2+1/x^2=527x/(x^2+x+1)-x/(x^2-x+1)=1/(x+1+1/x)-1/(x-1+1/x)=1/[(x+1/x)+1]-1/[(x+1/x)-1]=1/(23+1)-1/(23-1)=1/24-1/22=-1/264 【问题补充：如果已知条件不变,求根号x的平方+x+1分之x 减 根号x的平方-x+1分之x的值】根号[x/(x^2+x+1)]-根号[x/(x^2-x+1)]=根号[1/(x+1+1/x)]-根号[1/(x-1+1/x)]=根号[1/(x+1/x+1)]-根号[1/(x+1/x-1)]=根号(1/(23+1)]-根号[1/(23-1)]=1/根号24-1/根号22=(根号22-2根号6)/(4根号33）