Question

若x加x分之一等于3则x的4次方加x的4次方分之一等于多少

Answer 1

x+1/x=3
两边乘x
x²+1=3x
两边平方
x^4+2x²+1=9x²
x^4+1=7x²
两边平方
x^8+2x^4+1=49x^4
x^8+1=47x^4
两边除以x^4
x^4+1/x^4=47

Answer 2

1、3x/（x-3）²+x/x-3
=[3x+x(x-3)]/(x-3)²
=(3x+x²-3x)/(x-3)²
=x²/(x-3)²

2、（1+1/x-2）÷x²-1/2x-4
=[(x-1)/(x-2)]×[2(x-2)/(x+1)(x-1)]
=2/(x+1)

3、若1/x-1/y=2，求3x-2xy-3y/x-2xy-y的值
1/x-1/y=(y-x)/xy=2
y-x=2xy
x-y=-2xy
原式=[3(x-y)-2xy]/[(x-y)-2xy]
=(-6xy-2xy)/(-2xy-2xy)
=(-6-2)/(-2-2)
=2