方程1/x-2 - 1/x-4 = 1/x-3 - 1/x-5的解是x=7/2 ; 方程1/x-7 - 1/x-5 = 1/x-6 - 1/x-4的解是x=11/2(1)是猜想方程1/x-7 + 1/x-1 = 1/x-6 + 1/x-6 + 1/x-2的解;(2)猜想方程1/x-a - 1/x-b = 1/x-c - 1/x-d的解,并说明理由.(a,b,c,
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![方程1/x-2 - 1/x-4 = 1/x-3 - 1/x-5的解是x=7/2 ; 方程1/x-7 - 1/x-5 = 1/x-6 - 1/x-4的解是x=11/2(1)是猜想方程1/x-7 + 1/x-1 = 1/x-6 + 1/x-6 + 1/x-2的解;(2)猜想方程1/x-a - 1/x-b = 1/x-c - 1/x-d的解,并说明理由.(a,b,c,](/uploads/image/z/54953-17-3.jpg?t=%E6%96%B9%E7%A8%8B1%2Fx-2+-+1%2Fx-4+%3D+1%2Fx-3+-+1%2Fx-5%E7%9A%84%E8%A7%A3%E6%98%AFx%3D7%2F2+%3B+%E6%96%B9%E7%A8%8B1%2Fx-7+-+1%2Fx-5+%3D+1%2Fx-6+-+1%2Fx-4%E7%9A%84%E8%A7%A3%E6%98%AFx%3D11%2F2%EF%BC%881%EF%BC%89%E6%98%AF%E7%8C%9C%E6%83%B3%E6%96%B9%E7%A8%8B1%2Fx-7+%2B+1%2Fx-1+%3D+1%2Fx-6+%2B+1%2Fx-6+%2B+1%2Fx-2%E7%9A%84%E8%A7%A3%EF%BC%9B%EF%BC%882%EF%BC%89%E7%8C%9C%E6%83%B3%E6%96%B9%E7%A8%8B1%2Fx-a+-+1%2Fx-b+%3D+1%2Fx-c+-+1%2Fx-d%E7%9A%84%E8%A7%A3%2C%E5%B9%B6%E8%AF%B4%E6%98%8E%E7%90%86%E7%94%B1.%EF%BC%88a%2Cb%2Cc%2C)
方程1/x-2 - 1/x-4 = 1/x-3 - 1/x-5的解是x=7/2 ; 方程1/x-7 - 1/x-5 = 1/x-6 - 1/x-4的解是x=11/2(1)是猜想方程1/x-7 + 1/x-1 = 1/x-6 + 1/x-6 + 1/x-2的解;(2)猜想方程1/x-a - 1/x-b = 1/x-c - 1/x-d的解,并说明理由.(a,b,c,
方程1/x-2 - 1/x-4 = 1/x-3 - 1/x-5的解是x=7/2 ; 方程1/x-7 - 1/x-5 = 1/x-6 - 1/x-4的解是x=11/2
(1)是猜想方程1/x-7 + 1/x-1 = 1/x-6 + 1/x-6 + 1/x-2的解;
(2)猜想方程1/x-a - 1/x-b = 1/x-c - 1/x-d的解,并说明理由.(a,b,c,d表示不同的数,且a+d=b+c)
方程1/x-2 - 1/x-4 = 1/x-3 - 1/x-5的解是x=7/2 ; 方程1/x-7 - 1/x-5 = 1/x-6 - 1/x-4的解是x=11/2(1)是猜想方程1/x-7 + 1/x-1 = 1/x-6 + 1/x-6 + 1/x-2的解;(2)猜想方程1/x-a - 1/x-b = 1/x-c - 1/x-d的解,并说明理由.(a,b,c,
第一小题为X=4 第二题 X=a+c或b+d
1
1
(1):8/5
(2):x=a+c或x=b+c
(1)2/x-8=3/x-14 1/x=6 x=1/6
(2)这个方程无解。
(1/x-7)+(1/x-1)=(1/x-6)+(1/x-2)
1/(x-7)-1/(x-6)=1/(x-2)-1/(x-1)
(x-6-x+7)/[(x-7)(x-6)]=(x-1-x+2)/[(x-1)(x-2)]
(x-1)(x-2)=(x-7)(x-6)
x²-3x+2=x²-13x+42
10x=40
x=4
(...
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(1/x-7)+(1/x-1)=(1/x-6)+(1/x-2)
1/(x-7)-1/(x-6)=1/(x-2)-1/(x-1)
(x-6-x+7)/[(x-7)(x-6)]=(x-1-x+2)/[(x-1)(x-2)]
(x-1)(x-2)=(x-7)(x-6)
x²-3x+2=x²-13x+42
10x=40
x=4
(1/x+a)-(1/x+b)=(1/x+c)-(1/x+d)
(x+b-x-a)/[(x+a)(x+b)]=(x+d-x-c)/[(x+c)(x+d)]
(b-a)(x+c)(x+d)=(d-c)(x+a)(x+b)
因为a+d=b+c
所以b-a=d-c
x²+(c+d)x+cd=x²+(a+b)x+ab
x=(cd-ab)/(a+b-c-d)
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