www.fltk.net > 阅读并完成下列问题:方程x+1/x=2+1/2的解是x1=2,x2=1/2;x+1/x=3+1/3的...

阅读并完成下列问题:方程x+1/x=2+1/2的解是x1=2,x2=1/2;x+1/x=3+1/3的...

解:1.x+1/x+1=a+1/a+1(x不等于1) x+1/x=a+1/a2.x1=a,x2=1/a3.拼凑法,举一反三

x1=0 x2=2/3

先阅读下面的材料,然后回答问题:方程x+1/x=2+1/2的解为x1=2,x2=1/2;x+1/x=3+1/3的解为x1=3,x2=1/3;在解方程:y+(y+2)/y+1=10/3变形为X+1/X=A+1/A的形式求值

X-1/X=1又1/2 猜想:x=2,x=-1/2证明:X-1/X=1又1/2(x^2-1)/x=3/22(x^2-1)=3x2x^2-2=3x2x^2-3x-2=0 (x-2)(2x+1)=0 x=2,x=-1/2证明一般式X-1/X=n又n/(n+1)(x^2-1)/x=[n(n+1)+n]/(n+1)(x^2-1)/x=n(n+2)/(n+1)(n+1)(x^2-1)=n(n+2)x(n+1)x^2-n(n+2)x-(n+1)=0利用十字相乘法[(n+1)x-1]*[x-(n+1)]=0x=1/(n+1), x=n+1所以:X-1/X=n又n/(n+1)的解是x=1/(n+1), x=n+1

(x-x+1)/(x-1)=a+1/(a-1)x+1/(x-1)=a+1/(a-1)x-1+1/(x-1)=a-1+1/(a-1)所以x-1=a-1或x-1=1/(a-1)所以x1=a,x2=a/(a-1)

(1)x1=c.x2=m/c(2)等式两边同时减一.得x-1+2/(x-1)=a-1+2/(a-1)所以(x-1)1=a-1.即x1=a.(x-1)2=2/(a-2)即x2=1+2/(a一1)=(a+1)/(a-1)

方程x+1/x=2+1/2的解是x1=2,x2=1/2; x+1/x=3+1/3的解是x1=3,x2=1/3,观察上述方程的解,试猜想关于x的方程x+1/x=c+1/c的解是【x1=c,x2=1/c】把关于x的方程x+1/(x-1)=a+1/(a-1)变形为x+1/x=c+1/c的形式是【(x-1)+1/(x-1)=(a-1)+1/(a-1)】,方程的解是【x1=a,x2=1/a】,解决这个问题的数学思想是【方程两边同时加或减同一个数,等式依然成立】 很高兴为您解答,祝你学习进步!【学习宝典】团队为您答题.有不明白的可以追问!如果您认可我的回答.请点击下面的【选为满意回答】按钮,谢谢!

x+3/x=1+x-1

解【1】x-x+1=(x-2x+1)+x=(x-1)+x=(x-1)+(x-1)+1即:x-x+1=(x-1)+(x-1)+1∴(x-x+1)/(x-1)=[(x-1)+(x-1)+1]/(x-1)=(x-1)+1+[1/(x-1)]即原方程左边=(x-1)+1+[1/(

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