Question

Chứng minh rằng :

a , ( a - b ) + 9 c - d ) - ( a + c ) = - ( b + d )

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

Answer 1

Xem lại đề bài câu a

b) \(\left(a-b\right)-\left(c-d\right)+\left(b+c\right)=a+d\\ \Leftrightarrow a-b-c+d+b+c=a+d\\ \Leftrightarrow a+\left(b-b\right)+\left(c-c\right)+d=a+d\\ \Leftrightarrow a+d=a+d\\ \Leftrightarrow0=0\left(\text{luôn đúng}\right)\)

Ta được đpcm

Answer 2

a) \(\left(a-b\right)+\left(c-d\right)-\left(a+c\right)=-\left(b+d\right)\\ \Leftrightarrow a-b+c-d-a-c=-b-d\\ \Leftrightarrow\left(a-a\right)+\left(c-c\right)-b-d=-b-d\\ \Leftrightarrow-b-d=-b-d\\ \Leftrightarrow0=0\left(\text{luôn đúng}\right)\)

Ta được đpcm

Answer 3

nhắc bn đánh telex nhầm ( thành số 9, mk sửa lại nha)

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

↔ a - b + c - d - a - c = -(b + d)

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

↔ 0 + 0 - b - d = -(b + d)

↔ 0 + 0 -(b + d) = -(b + d)

↔ -(b + d) = -(b + d)

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

↔ a - b - c + d + b + c = a + d

↔ a + (b - b) + (c - c) + d = a + d

↔ a + 0 + 0 + d = a + d

↔ a + d = a + d

Answer 4

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

↔ a - b + c - d - a - c = -(b + d)

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

↔ 0 + 0 - b - d = -(b + d)

↔ 0 + 0 -(b + d) = -(b + d)

↔ -(b + d) = -(b + d)

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

↔ a - b - c + d + b + c = a + d

↔ a + (b - b) + (c - c) + d = a + d

↔ a + 0 + 0 + d = a + d

↔ a + d = a + d

Answer 5

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

↔ a - b + c - d - a - c = -(b + d)

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

↔ 0 + 0 - b - d = -(b + d)

↔ 0 + 0 -(b + d) = -(b + d)

↔ -(b + d) = -(b + d)

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

↔ a - b - c + d + b + c = a + d

↔ a + (b - b) + (c - c) + d = a + d

↔ a + 0 + 0 + d = a + d

↔ a + d = a + d