Question

1.已知:1/x-2/y=3,则(4x+13xy-2y)/(y+3xy-2x)=? 2.分解因式:a`2(b-c)+b`2(c-a)+c`2(a-b)=?

3.解方程 x`2+1/(x`2)-3.5(x-1/x)+1=0
4.已知实数属于a、b、c、满足a+b+c=11与1/(a+b)+1/(b+c)+1/(c+a)==13/17，求a/(b+c)+b/(a+c)+c/(a+b)的值。

Answer 1

1. 1/x-2/y=3 ，y-2x=3xy
(4x+13xy-2y)/(y+3xy-2x)
=[2(2x-y)+13xy]/(3xy+3xy)
=(-6xy+13xy)/6xy
=7/6

2.a^2(b-c)+b^2(c-a)+c^2(a-b)
=a^2b-a^2c+b^2c-ab^2+ac^2-bc^2
=ab(a-b)-c(a+b)(a-b)+c^2(a-b)
=(a-b)(ab-ca-bc+c^2)
=(a-b)[a(b-c)-c(b-c)]
=(a-b)(a-c)(b-c)

4. a/(b+c)+b/(a+c)+c/(a+b)
=[11-(b+c)]/(b+c)+[11-(a+c)]/(a+c)+[11-(a+b)]/(a+b)
=11/(b+c)-1+11/(a+c)-1+11/(a+b)-1
=11[1/(a+b)+1/(b+c)+1/(c+a)]-3
=11×13/17-3
=92/17

不好意思 .第三题还没做出来...

追问

麻烦了~谢谢 ...不过 你能把第3个做出来不....谢~~

追答

3. 设 1/x=y ∴ 1/x^2=y^2, xy=1
x^2+1/(x^2)-3.5(x-1/x)+1=0
变为 x^2+y^2-3.5(x-y)+1=0
x^2+y^2-2xy+2xy-3.5(x-y)+1=0
(x-y)^2-3.5(x-y)+3=0
(x-y-2)(x-y-1.5)=0
∴x-y=2 或 x-y=1.5
即为 x-1/x=2 或 x-1/x=1.5 接下来的楼主自己可以算完吧？

Answer 2

1. (1/x-2/y)xy=3xy ——》y-2x=3xy
(4x+13xy-2y)/(y+3xy-2x)
=[2(2x-y)+13xy)/(3xy+3xy)
=(-6xy+13xy)/6xy
=7/6

劝你还是自己动脑筋做 不会就空着

Answer 3

7/6

Answer 4

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