1.已知x+1/x=4,求x²+1/x²和(x-1/x)²的值 2.已知x²+3x1.已知_数学解答

1.已知x+1/x=4,求x²+1/x²和(x-1/x)²的值 2.已知x²+3x
1.已知x+1/x=4,求x²+1/x²和(x-1/x)²的值
2.已知x²+3x-1=0,求x+1/x的值

人气：493 ℃　时间：2020-03-13 16:43:08

解答

1.x+1/x=4两边平方,x²+1/x²+2=16x²+1/x²=14(x-1/x)²=(x+1/x)²-4=16-4=122.x²+3x-1=0x²-1=3xx-1/x=3两边平方x²+1/x²-2=9x²+1/x²=11(x+1/x)²=x...x²+1/x²+2=16
x²+1/x²=14

(x-1/x)²=(x+1/x)²-4=16-4=12

为什么要+2和-4？(x-1/x)²
=x²+1/x²-2*x*1/x
=x²+1/x²+2*x*1/x-4*x*1/x
=(x+1/x)²-4
=16-4
=12

(x+1/x)²
=x²+1/x²+2*x*1/x
=11+2
=13