Question

Bài 1:

Chứng minh đẳng thức:
– (–m + n + p) + (n + p – 3) = (n – p + 8) – (11 – m + n) + p.

Bài 2;

Cho A = b – c – 4; B = b – a;
C = –b – c + 1; D = a + b – 5.

Chứng minh rằng: A – B = C + D.

Các bạn giúp mik

Answer 1

Bài 1:

\(-\left(-m+n+p\right)+\left(n+p-3\right)=\left(n-p+8\right)-\left(11-m+n\right)+p\\ \Leftrightarrow m-n-p+n+p-3=n-p+8-11+m-n+p\\ \Leftrightarrow\left(n-n\right)+\left(p-p\right)+m-3=\left(n-n\right)+\left(p-p\right)+m+\left(8-11\right)\\ \Leftrightarrow m-3=m+\left(-3\right)\\ \Leftrightarrow m-3=m-3\\ \Leftrightarrow0=0\left(\text{luôn đúng}\right)\)

Ta được đpcm

Bài 2:

\(A-B=\left(b-c-4\right)-\left(b-a\right)\\ A-B=b-c-4-b+a\\ A-B=\left(b-b\right)+a-c-4\\ A-B=a-c-4\left(1\right)\)

\(C+D=\left(-b-c+1\right)+\left(a+b-5\right)\\ C+D=-b-c+1+a+b-5\\ C+D=\left(b-b\right)+a-c+\left(1-5\right)\\ C+D=a-c+\left(-4\right)\\ C+D=a-c-4\left(2\right)\)

(1) (2) \(\Rightarrow A-B=C+D\left(đpcm\right)\)