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1. A = 75(42004 + 42003 +...+ 42 + 4 + 1) + 25
A = 25 . [3 . (42004 + 42003 +...+ 42 + 4 + 1) + 1]
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 3 + 1)
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 4)
A = 25 . 4 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1)
A =100 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1) \(⋮\) 100
a) \(x\ge\frac{2}{3}\Rightarrow3x-2\ge0\Rightarrow\left|3x-2\right|=3x-2\)
\(\Rightarrow P=\frac{1}{2}-\frac{1}{2}\left(x:\frac{1}{6}-\frac{1}{4}\right)-2\left(3x-2\right)\)
\(\Rightarrow P=\frac{1}{2}-\frac{1}{2}\left(6x-\frac{1}{4}\right)-6x+4\)
\(\Rightarrow P=\frac{4}{8}-3x+\frac{1}{8}-6x+\frac{32}{8}\)
\(\Rightarrow P=\frac{37}{8}-9x\)
b) \(x< \frac{2}{3}\Rightarrow3x-2< 0\Rightarrow\left|3x-2\right|=2-3x\)
\(\Rightarrow P=\frac{1}{2}-\frac{1}{2}\left(x:\frac{1}{6}-\frac{1}{4}\right)-2\left(2-3x\right)\)
\(\Rightarrow P=\frac{1}{2}-\frac{1}{2}\left(6x-\frac{1}{4}\right)-4+6x\)
\(\Rightarrow P=\frac{4}{8}-3x+\frac{1}{8}-\frac{32}{8}+6x\)
\(\Rightarrow P=\frac{-27}{8}+3x\)
Khi \(B=-\frac{3}{5}\)ta có :
\(B=\left|x-\frac{1}{7}\right|-\left|x+\frac{3}{5}\right|+\frac{4}{5}\)
\(B=\left|-\frac{3}{5}-\frac{1}{7}\right|-\left|-\frac{3}{5}+\frac{3}{5}\right|+\frac{4}{5}\)
\(B=-\frac{26}{35}-0+\frac{4}{5}\)
\(B=-\frac{26}{35}+\frac{4}{5}\)
\(B=\frac{2}{35}\)
\(B=\left|\frac{-3}{5}-\frac{1}{7}\right|-\left|\frac{-3}{5}+\frac{3}{5}\right|+\frac{4}{5}=\frac{26}{35}+\frac{4}{5}=\frac{2}{35}\)
a) \(P=1-\frac{1}{4}\left(10x-\frac{15}{4}\right)-6x+8\)
\(P=\frac{159}{16}-\frac{17x}{2}\)
b) \(P=1-\frac{1}{4}\left(10x-\frac{15}{4}\right)-8+6x\)
\(P=\frac{7x}{2}-\frac{97}{16}\)