Question

Chứng minh rằng:
a)  (a-b) - (c - d ) + (b+ c) = c + d
b) Nếu (a + b -  c) -  (a - b + c) = a + (- b - a + c ) thì b = c

Answer 1

Lời giải:

a.

$(a-b)-(c-d)+(b+c)=a-b-c+d+b+c=(a+d)+(-b+b)+(-c+c)$

$=a+d+0+0=a+d$

b.

$(a+b-c)-(a-b+c)=a+(-b-a+c)$

$a+b-c-a+b-c=a-b-a+c$

$(a-a)+(b+b)-(c+c)=(a-a)-b+c$

$2b-2c=-b+c$

$2b+b=2c+c$

$3b=3c$

$b=c$ (đpcm)