Question

高一数学 求详细解。最好有图。谢谢

Answer 1

因为x+1/x=3,则(x+1/x)^2=9,即：x^2+2+(1/x)^2=9,解得：x^2+(1/x)^2=7
因为x^2-(1/x^2)=(x+1/x)(x-1/x)
则将(x-1/x)平方得：(x-1/x)^2=x^2-2+(1/x)^2=7-2=5,所以(x-1/x)=正负根号5
所以x^2-(1/x)^2=正负3乘根号5

Answer 2

x+1/x=3

1. [x^(1/2)+x^(-1/2)]^2
=x+2+1/x=3+2=5
x^(1/2)+x^(-1/2)=5^(1/2)

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

3. x^2-x^(-2)
=(x+1/x)(x-1/x)
=3(x-1/x)
(x-1/x)^2=x^2-2+1/x^2=7-2=5
x-1/x=5^(1/2),或-5^(1/2)
x^2-x^(-2)=3*5^(1/2),
或-3*5^(1/2)