Question

初中数学题3道，利用“整体思想”求值

急急急

Answer 1

8. 解: 因为 根号x+1/根号x=2,
所以 x+2+1/x=4
x+1/x=2
x^2+2+1/x^2=4
x^2+1/x^2=2
所以 根号(x^2+1/x^2+14)
=根号(2+14)
=根号16
=4.
9.解: 因为 x=1--根号2, y=1+根号2
所以 x--y=--2根号2, xv=--1,
所以 x^2+y^2--xy--2x+2y=x^2--2xy+y^2--2x+2y+xy
=(x--y)^2--2(x--y)+xy
=8+4根号2--1
=7+4根号2.
10.解: 因为 x=3+2根号2, y=3--2根号2,
所以 x+y=6, xy=1,
所以 x/y+y/x--4=(x^2+y^2+2xy)/xy--6
=(x+y)^2/xy--6
=36/1--6
=30.

Answer 2

x^(1/2)-1/x^(1/2) = 2
两边 平方
x+1/x-2=4
x^2+1/x^2 = (x+1/x)^2-2=36-2=34
x^2+1/x^2+14 = 48
开根号 = 4根号3

9.
xy=-1 x = -1/y

x^2+y^2-xy-2x+2y
=x^2+1/x^2+1-2x-2/x
=(x^2-2x+1)+(1/x^2-2/x+1)-2+1
=(x-1)^2+(1/x-1)^2-1
=2+2-1=3
10
x/y+y/x-4
=(x^2+y^2)/xy-4
=(x+y)^2/xy-2-4
=36/1-6 = 30

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