Question

1, Chứng minh đẳng thức :

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

b) (a + b) - (b - a) + c = 2a + c

c) -( a + b - c) + (a- b- c) = -2b

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

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

2, So sánh P và Q

P = a+ {[( a - 3 ) - (-a - 2)]}

Q= [a + (a +3)] - [( a + 2) - ( a - 2)]

Answer 1

1, Chứng minh đẳng thức :

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

(a - b + c) - (a + c)

=a-b+c-a-c

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

=0+0-b

=-b

b) (a + b) - (b - a) + c = 2a + c

(a + b) - (b - a) + c

=a+b-b+a+c

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

=2a+0+c

=2a+c

c) -( a + b - c) + (a- b- c) = -2b

-( a + b - c) + (a- b- c)

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

=[a+(-a)]+[c+(-c)]-b-b

=0+0-(b+b)

=-2b

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

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

=ab+ac-(ab+ad)

=(ab-ab)+ac-ad

=0+ac-ad

=a(c-d)

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

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

=ab-ac+ad+ac

=(ac+(-ac))+ad+ab

=0+ad+ab

=a(d+b)

Answer 2

1

a) \( (a - b + c) - (a + c) \)

\(=\left(a+c-b\right)-\left(a+c\right)\)

\(=\left[\left(a-c\right)-\left(a-c\right)\right]-b\)

\(=0-b\)

\(=-b\)

b) \( (a + b) - (b - a) + c \)

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

\(=\left(a+a\right)+\left(b-b\right)+c\)

\(=\left(a+a\right)-0+c\)

\(=a+a+c\)

\(=2a+c\)

2

\(P=a+ [( a - 3 ) - (-a - 2)]\)

\(P=a+a-3+a+2\)

\(P=a+a+a-3+2\)

\(P=3a-3+2\)

\(P=0+2\)

\(P=2\)

\(Q=[a + (a +3)] - [( a + 2) - ( a - 2)]\)

\(Q=a+a+3-a-2-a+2\)

\(Q=a+a+3-a+\left(-2-a+2\right)\)

\(Q=2a+3-a+a\)

\(Q=2a+3-2a\)

\(Q=3\)

Vì \(P=2;Q=3\Rightarrow P< Q\)