中二數學Prove

determine whether each of the followingequations is an identity or not.
1. 6x－3x=x+2x
Sol
6x－3x=3x
x+2x=3x
3x=3x
(is)

2. －3(x－5)=－(3x+15)
Sol
－3(x－5)
=－3x+15
－(3x+15)
=－3x－15
(not)

3. (x－1)(x+4)=x^2－3x－4
Sol
(x－1)(x+4)
=x(x+4)－(x+4)
=x^2+4x－x－4
=x^2+3x－4
(not)

你好~
1.
L.H.S (left hand side) =6x - 3x
=3x
=x + 2x
R.H.S (right hand side) =x + 2x

∴6x - 3x=x + 2x is an identity.


2.
L.H.S = -3(x - 5)
= -3x + 15
= -(3x + 15)
R.H.S = -(3x + 15)


∴-3(x - 5)=-(3x + 15) is an identity.


3.
L.H.S = (x - 1)(x + 4)
= x² + 4x - x - 4
= x² + 3x - 4
R.H.S = x² - 3x - 4

∴(x - 1)(x + 4)=x² - 3x - 4 is not an identity.


希望幫到你~Y(^_^)Y

2012-10-13 12:39:19 補充：
sorry~
第2題錯左、答案如下
2.
L.H.S = -3(x - 5)
= -3x + 15
= -(3x + 15)
R.H.S = -(3x + 15)
= -3x - 15


∴-3(x - 5)=-(3x + 15) is not an identity.

Questions and Answers :

Determine whether each of the following equations is an identity or not.
1) 6x-3x=x+2x
L.H.S. = 6x-3x
= 3x
= x+2x
= R.H.S.
Therefore, 6x-3x ≡ x+2x is an identity.

2) -3(x-5)=-(3x+15)
L.H.S. = -3(x-5)
= 15-3x
R.H.S. = -(3x+15)
= -15-3x
L.H.S. ≠ R.H.S.
Therefore, -3(x-5) ≡ -(3x+15) is NOT an identity.

3) (x-1)(x+4)=x^2-3x-4
L.H.S. = (x-1)(x+4)
= x^2+3x-4
≠ R.H.S.
Therefore, (x-1)(x+4) ≡ x^2-3x-4 is NOT an identity.

1. LHS = 6x - 3x = 3x
RHS = x+2x = 3x
Since LHS = RHS
So the equation is an identity.

2. LHS = -3(x - 5) = 15-3x
RHS = -(3x+15) = -15-3x
Since LHS =/= RHS
So the equation is not an identity.

3. LHS = (x-1)(x+4)= x^2+3x-4
RHS = x^2-3x-4
Since LHS =/= RHS
So the equation is not an identity.

Hope I can help you =)