Question

已知x+1/x=3，求x^2+1/x^2和（x-1/x）^2的值

快一点，有追加

Answer 1

解： 将等式两边平方的：x^2+2+1/x^2=9 所以x^2+1/x^2=7
将（x-1/x)^2展开得：x^2-2+1/x^2=7-2=5

Answer 2

x^2+1/x^2
=(x+1/x)^2-2
=4

（x-1/x）^2
=x^2+1/x^2-2
=4-2
=2

Answer 3

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

（x-1/x）^2
=(x+1/x)^2-4
=9-4
=5

Answer 4

x^2+1/x^2=(x+1/x)^2-2=3^2-2=9-2=7

（x-1/x）^2=x^2-2+1/x^2=x^2-2+1/x^2=7-2=5