(1) (x-1/x)^2=3^2=9 x^2+1/x^2-2=9 x^2+1/x^2=11 (x^2+1/x^2)^2=11^2 xZ^4+1/x^4+2=121 x^4+1/x^4=121-2=119
(2) 2xy=(x+y)^2-(x^2+y^2)=16-10=6 (x-y)^2=x^2+y^2-2xy=10-6=4 x-y=±2 x^2-y^2=(x-2)(x+2)=±8
∵x-1/x=3
∴(x-1/x)^2=9
x^2+1/x^2=11
∴x^4+1/x^4
=(x^2+1/x^2)^2-2
=11^2-2
=119
2.2xy=(x+y)^2-(x^2+y^2)
=16-10=6
(x-y)^2=x^2+y^2-2xy
=10-[(x+y)^2-(x^2+y^2)]
=10-[16-10]
=10-6
=4
x-y=√x^2+y^2-2xy
=√10-[(x+y)^2-(x^2+y^2)]
=√10-[16-10]
=√4
=2
x^2-y^2=(x+y)(x-y)
=4*√x^2+y^2-2xy
=4*√10-[(x+y)^2-(x^2+y^2)]
=4* √10-[16-10]
=4*√4
=4*2=8)
(*是乘的意思,x^2是x的2次方)
(1)119
(2)6 4 2 8