Question

已知x+3/x+2=1/ 根号2+1 求x-3/2x-4÷(5/x-2-x-2)的值

Answer 1

(x+3)/(x+2)=1/(√2+1)
x+2=(x+3)(√2+1)
x+2=(x+2+1)(√2+1)
x+2=(√2+1)(x+2)+√2+1
(x+2)√2=√2+1
x+2=(√2+1)/√2=(2+√2)/2
x+3=(4+√2)/2

原式=(x-3)/(2x-4)÷[5/(x-2)-x-2)
=(x-3)/(2x-4)÷(9-x^2)/(x-2)
=(x-3)/[2(x-2)]*[(x-2)/(9-x^2)]
=(x-3)/[2(x-2)]*(x-2)/[(3-x)(x+3)]
=-1/[2(x+3)]
=-1/[2(4+√2)/2]
=(√2-4)/12

忍不住问一句,你的题目有没有写错?

追问

我也觉得出题出得很奇怪，但我核实过了确实老师是这么打印的，就不知他打印错没有

追答

哦,就是觉得有点烦,不过解题思路都是一样的

Answer 2

x+3/x+2=1/ 根号2+1
x+2=(x+3)(√2+1)
x+2=(x+2+1)(√2+1)
x+2=(√2+1)(x+2)+√2+1
(x+2)√2=√2+1
x+2=(√2+1)/√2=(2+√2)/2
x+3=(4+√2)/2
x-3/2x-4÷(5/x-2-x-2)==(x-3)/(2x-4)÷[5/(x-2)-x-2)
=(x-3)/(2x-4)÷(9-x^2)/(x-2)
=(x-3)/[2(x-2)]*[(x-2)/(9-x^2)]
=(x-3)/[2(x-2)]*(x-2)/[(3-x)(x+3)]
=-1/[2(x+3)]
=-1/[2(4+√2)/2]
=(√2-4)/12

计算这么烦