(1)若x-1/x=3,则x^2+1/x^2=(2)已知x/2=y/3=z/4,则2x+y-z/3x-2y+z=(3)计算,(1/a-1)-1-a

Question

(1)若x-1/x=3,则x^2+1/x^2=_____________
(2)已知x/2=y/3=z/4,则2x+y-z/3x-2y+z=____________
(3)计算,
(1/a-1)-1-a

Answer 1

1)若x-1/x=3,则x^2+1/x^2=_____________
平方x^2-2*x*1/x+1/x^2=3^2=9
x^2+1/x^2=9+2=11
(2)已知x/2=y/3=z/4,则2x+y-z/3x-2y+z=____________
x/2=y/3=z/4=k
x=2k,y=3k,z=4k
(2x+y-z)/(3x-2y+z)
=(4k+3k-4k)/(6k-6k+4k)
=3k/4k
=3/4
(3)计算,
(1/a-1)-1-a
=1/(a-1)-(a+1)
=[1-(a-1)(a+1)]/(a-1)
=(1-a^2+1)/(a-1)
=(2-a^2)/(a-1)