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The latest version of the MultiECUScan software supplied on CD.. 6 Keygen 6,6/10 8466 votes Our MultiECUScan bundle package supports fault code.Q:
Interchanging two identities
I have a problem with solving following equation $$S=x(1-x)+y(1-y)+xy$$
In textbook are given several identities that can be used to solve this but i have no idea how to use them.
Two identities are: $x(1-x)=xy$ and $(x-y+1)(y-x)=0$
thanks in advance
A:
With your identities
$$(x-y+1)(y-x)=0$$
$$xy=x(1-y)=x(1-x)y=x(1-x)y$$
$$x(1-y) = 0 \tag{1}$$
Using $(1)$
$$xy=x(1-y)$$
$$xy(1-x)=0 \tag{2}$$
Multiplying $(2)$ by $y$ on the left side and $(1)$ by $x$ on the right side
$$xy(1-x)y=0$$
$$xy(1-x)y=y(1-x)xy$$
$$xy(1-x)=y(1-x) \tag{3}$$
Multiplying $(3)$ by $1-x$ on the left side
$$xy(1-x)(1-x)=0$$
$$xy(1-x)^2=0 \tag{4}$$
Using $(4)$
$$(1-x)^2=0$$
$(1-x)=0$
$1-x=0 \implies x=1$
Thus $S=1$.
A:
$S-x(1-x) = y(1-y)$
$xy = x(1-y)$
$x(1-y)=0$
$y = 1$
So $S = 1$
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