Question

已知a与b互为相反数，且A-B=4/5.求（a-ab+b)/(aa+ab+1)的值

已知a与b互为相反数，且A-B=4/5.求（a-ab+b)/(aa+ab+1)的值

Answer 1

a、b互为相反数，则a + b = 0
a - ab + b = (a + b) - ab = -ab
aa + ab +1 = a(a + b) +1 = a * 0 +1 = 1

所以（a -ab+b)/(aa + ab +1) = -ab = aa
因为a -b = 4/5，a + b = 0，所以a = 2/5, b = -2/5
所以 aa = 4/25

Answer 2

A与B互为相反数
A=-B

A减B的绝对值 等于5分之4
|A-B|=4/5
|-B-B|=|2B|=4/5
2B=±4/5
B=±2/5

A=2/5,B=-2/5或A=-2/5,B=2/5
所以 AB=-2/5*2/5=-4/25

(A-AB+B)/(A^2+AB+1)
=[(A+B)-AB]/[A(A+B)+1]
=[0-(-4/25)]/(A*0+1)
=4/25

Answer 3

∵A与B互为相反数，且A-B=4/5
∴2A=4/5
∴A=2/5 B=-2/5 1 （A-AB+B）÷（A^2+AB+1）=[0.4-0.4*(-0.4)-0.4]÷[0.4^2+0.4*(-0.4)+1]=4/25

Answer 4

由题意可知
a+b=0
a-b=4/5
所以a=2/5 b=-2/5
原式=4/25除以1=4/25

Answer 5

a,b相反数，则(a-ab+b)/(a^2+ab+1)=a^2/(a^2-a^2+1)=(2/5)^2=4/25