Question

已知x+x的负一次方=3 求x的1/2次方加x的负1/2次方的值 求x的2次方-x的负2次方的值

Answer 1

因为x+x^(-1)=[x^(1/2)+x^(-1/2)]^2-2。而x+x^(-1)=3
所以[x^(1/2)+x^(-1/2)]^2-2=3得到[x^(1/2)+x^(-1/2)]^2=5
故x^(1/2)+x^(-1/2)=根号5

x^2-x^(-2)=[x+x^(-1)]*[x-x^(-1)]=[x+x^(-1)]*[x^(1/2)+x^(-1/2)]*[x^(1/2)-x^(-1/2)]
已知x+x^(-1)=3,x^(1/2)+x^(-1/2)=根号5
而[x^(1/2)-x^(-1/2)]=根号内“[x^(1/2)+x^(-1/2)]^2-4”=1
故x^2-x^(-2)=[x+x(-1)]*[x-x(-1)]=[x+x(-1)]*[x^(1/2)+x^(-1/2)]*[x^(1/2)-x^(-1/2)]=3*根号5*1=3倍根号5

Answer 2

(x+1/x)^2
=x^2+1/x^2+2
=9
x^2+1/x^2 = 7

(x^(1/2)+x^(-1/2))^2
=x+1/x+2
=3
x^(1/2)+x^(-1/2)=1