简便计算 1 1 4 x 1 51 1 5 x

2021-03-12 14:37:31 字数 2985 阅读 4991

1楼:匿名用户

令a=1/2+1/3+1/4,b=1/2+1/3+1/4+1/5(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)

=(1+a)*b-(1+b)*a

=b+ab-a-ab

=b-a

=1/5

2楼:匿名用户

为了简述方便

假设1/2+1/3+1/4=a

那么原式=(1+a)(a+1/5)-(1+a+1/5)a=a+1/5+a*a+a/5-a-a*a-a/5=1/5

3楼:匿名用户

(1+1/2+1/3+1/4)(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)

=(1+1/2+1/3+1/4)(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)(1/2+1/3+1/4)-1/5(1/2+1/3+1/4)

=(1+1/2+1/3+1/4)(1/2+1/3+1/4+1/5-1/2-1/3-1/4)-1/5(1/2+1/3+1/4)

=(1+1/2+1/3+1/4)(1/5)-1/5(1/2+1/3+1/4)

=1/5*(1+1/2+1/3+1/4-1/2-1/3-1/4)

=1/5

4楼:匿名用户

(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)

=(1+1/2+1/3+1/4)x[(1/2+1/3+1/4)+(1/5)]-[(1+1/2+1/3+1/4)+(1/5)]x(1/2+1/3+1/4)

=(1+1/2+1/3+1/4)x(1/2+1/3+1/4)+(1+1/2+1/3+1/4)x(1/5)-(1+1/2+1/3+1/4)x(1/2+1/3+1/4)-(1/5)x(1/2+1/3+1/4)

=(1+1/2+1/3+1/4)x(1/5)-(1/5)x(1/2+1/3+1/4)

=1/5

简便计算(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)

5楼:叫啥知不道

设a=(1/2+1/3+1/4),b=(1/2+1/3+1/4+1/5)

原式=(1+a)*b-(1+b)*a

=b+ab-a-ab

=b-a

=1/5

小学数学 计算:(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)x(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)

6楼:匿名用户

(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)

中间该是减号.

设1/2+1/3+1/4+1/5=m,1/2+1/3+1/4=n原式=(1+n)*(m)-(1+m)*n

=m+nm-n-nm

=m-n

=1/5

7楼:匿名用户

中间是减号吧

(1+1/2+1/3+1/4)(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)

=[1+(1/2+1/3+1/4)][(1/2+1/3+1/4)+1/5]-[(1+1/5) + (1/2+1/3+1/4)] * (1/2+1/3+1/4)

令x=1/2+1/3+1/4)

则原式=(1+x)(x+1/5) - ((1+1/5)+x)*x= x + 1/5 +x*x +x/5 -[x*x +x +x/5]= x+1/5+x*x+x/5 -x*x -x -x/5= 1/5

8楼:發生以後

(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)

=1 x(1/2+1/3+1/4+1/5)+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -[1 x(1/2+1/3+1/4)+(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)]

=1 x(1/2+1/3+1/4+1/5)+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -1 x(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)

=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)=1/5

9楼:骗了他吗

(1+1/2+1/3+1/4)(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)

=[1+(1/2+1/3+1/4)][(1/2+1/3+1/4)+1/5]-[(1+1/5) + (1/2+1/3+1/4)] * (1/2+1/3+1/4)

令x=1/2+1/3+1/4)

则原式=(1+x)(x+1/5) - ((1+1/5)+x)*x= x + 1/5 +x*x +x/5 -[x*x +x +x/5]= x+1/5+x*x+x/5 -x*x -x -x/5= 1/5

简便计算(1+2/1-3/1+4/1)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)

10楼:新野旁观者

(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)

=(1/2+1/3+1/4+1/5)+(1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)

=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)=1/5

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