阅读下列材料:x+1/x=c+1/c的解是:x1=c,x2=1/c;(x+1/x=c+1/c)的解是:x1=c,x2=-1/c;x+2/x=c+2/c阅读下列材料:x+ 1/x=c+ 1/c的解是:x1=c,x2=1/c;(x- 1/x=c- 1/c)的解是:x1=c,x2= - 1/c;x+ 2/x=c+ 2/c的解是:x1=c,x2=2/c;x+ 3/x=c+ 3/c
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![阅读下列材料:x+1/x=c+1/c的解是:x1=c,x2=1/c;(x+1/x=c+1/c)的解是:x1=c,x2=-1/c;x+2/x=c+2/c阅读下列材料:x+ 1/x=c+ 1/c的解是:x1=c,x2=1/c;(x- 1/x=c- 1/c)的解是:x1=c,x2= - 1/c;x+ 2/x=c+ 2/c的解是:x1=c,x2=2/c;x+ 3/x=c+ 3/c](/uploads/image/z/5245629-69-9.jpg?t=%E9%98%85%E8%AF%BB%E4%B8%8B%E5%88%97%E6%9D%90%E6%96%99%EF%BC%9Ax%2B1%2Fx%3Dc%2B1%2Fc%E7%9A%84%E8%A7%A3%E6%98%AF%EF%BC%9Ax1%3Dc%2Cx2%3D1%2Fc%3B%28x%2B1%2Fx%3Dc%2B1%2Fc%29%E7%9A%84%E8%A7%A3%E6%98%AF%3Ax1%3Dc%2Cx2%3D-1%2Fc%3Bx%2B2%2Fx%3Dc%2B2%2Fc%E9%98%85%E8%AF%BB%E4%B8%8B%E5%88%97%E6%9D%90%E6%96%99%EF%BC%9Ax%2B+1%2Fx%3Dc%2B+1%2Fc%E7%9A%84%E8%A7%A3%E6%98%AF%EF%BC%9Ax1%3Dc%2Cx2%3D1%2Fc%3B%28x-+1%2Fx%3Dc-+1%2Fc%29%E7%9A%84%E8%A7%A3%E6%98%AF%3Ax1%3Dc%2Cx2%3D+-+1%2Fc%3Bx%2B+2%2Fx%3Dc%2B+2%2Fc%E7%9A%84%E8%A7%A3%E6%98%AF%3Ax1%3Dc%2Cx2%3D2%2Fc%3Bx%2B+3%2Fx%3Dc%2B+3%2Fc)
阅读下列材料:x+1/x=c+1/c的解是:x1=c,x2=1/c;(x+1/x=c+1/c)的解是:x1=c,x2=-1/c;x+2/x=c+2/c阅读下列材料:x+ 1/x=c+ 1/c的解是:x1=c,x2=1/c;(x- 1/x=c- 1/c)的解是:x1=c,x2= - 1/c;x+ 2/x=c+ 2/c的解是:x1=c,x2=2/c;x+ 3/x=c+ 3/c
阅读下列材料:x+1/x=c+1/c的解是:x1=c,x2=1/c;(x+1/x=c+1/c)的解是:x1=c,x2=-1/c;x+2/x=c+2/c
阅读下列材料:x+ 1/x=c+ 1/c的解是:x1=c,x2=1/c;
(x- 1/x=c- 1/c)的解是:x1=c,x2= - 1/c;
x+ 2/x=c+ 2/c的解是:x1=c,x2=2/c;x+ 3/x=c+ 3/c的解是:x1=c,x2=3/c;_.
① 请观察上述方程与解的特征,猜想方程x+ m/x=c+ m/c (m≠0)的解.并进行验证.
② x+(2/x-1)=a+(2/a-1) 利用上面的结论解.
阅读下列材料:x+1/x=c+1/c的解是:x1=c,x2=1/c;(x+1/x=c+1/c)的解是:x1=c,x2=-1/c;x+2/x=c+2/c阅读下列材料:x+ 1/x=c+ 1/c的解是:x1=c,x2=1/c;(x- 1/x=c- 1/c)的解是:x1=c,x2= - 1/c;x+ 2/x=c+ 2/c的解是:x1=c,x2=2/c;x+ 3/x=c+ 3/c
(1)方程的特征是x+n/x=c+n/c
解为x1=c,x2=n/c.
(2)x+2/(x-1)=a+2/(a-1)可
变换为(x-1)+2/(x-1)=(a-1)+2/(a-1)(两边各减1)
猜测其解为x1-1=a-1,x2-1=2/(a-1)
即x1=a,x2=2/(a-1)+1=(a+1)/(a-1)
(验证的话就是带入猜测的x1 x2的值看两边是否相等)
x1=a的时候,两边显然相等
x2=(a+1)/(a-1)的时候
左边=2/(a-1)+1+a-1=右边,
所以也相等
∴两个都是方程的根