Question

1.已知x+1/x=4,求x²+1/x²和(x-1/x)²的值 2.已知x²+3

Answer 1

1.x+1/x=4

两边平方,x²+1/x²+2=16

x²+1/x²=14

(x-1/x)²=(x+1/x)²-4=16-4=12

2.x²+3x-1=0

x²-1=3x

x-1/x=3

两边平方

x²+1/x²-2=9

x²+1/x²=11

(x+1/x)²=x²+1/x²+2=11+2=13

x+1/x=±根号13