\(x=-37\)

A=\(\frac{63x101x37-37x101x63}{1+2+3+..+2014}\)(vì 636363=63x10101 và 373737=37x101x63)

A\(\frac{0}{1+2+3+4...+2014}\)

A=0

\(A=\frac{636363\times37-373737\times63}{1+2+3+....+2014}\)

\(A=\frac{63\times10101\times37-373737\times63}{1+2+3+......+2014}\)

\(A=\frac{373737\times63-373737\times63}{1+2+3+.....+2014}\)

\(A=\frac{0}{1+2+3+.....+2014}\)

\(A=0\)

HOK TOT

Mình nghĩ đề thế này mới tính hợp lí được

2 ) B = \(1\frac{6}{41}.\left(\frac{12+\frac{12}{19}-\frac{12}{37}-\frac{12}{53}}{3+\frac{3}{19}-\frac{3}{37}-\frac{3}{53}}:\frac{4+\frac{4}{17}+\frac{4}{19}+\frac{4}{2006}}{5+\frac{5}{17}+\frac{5}{19}+\frac{5}{2006}}\right).\frac{124242423}{237373735}\)

B = 47/41 . ( 12/3 : 4/5 ) . 123/235

B = 47/41 . ( 4 : 4/5 ) . 123/235

B = 47/41 . 5 . 123/235

B = \(\frac{47.5.123}{41.235}\)

B = 3

1 ) A = \(\frac{636363.37-373737.63}{1+2+3+...+2006}\)

A = \(\frac{63.10101.37-37.10101.63}{1+2+3+...+2006}\)

A = \(\frac{0}{1+2+3+...+2006}\)

A = 0

37/42+37/56+37/72 = 37(1/42+1/56+1/72)=37( 1/6.7 + 1/7.8 + 1/8.9 )= 37( 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9)= 37( 1/6 - 1/9)= 37.1/18=37/18

B = 37/42 + 37/56 + 37/72 

B = 37/18

37/42 + 37/56 +37/72=37/24 + 37/72= 37/18

 Kết quả : 

    \(=\frac{37}{53}x\frac{23}{48}x\frac{53}{37}x\frac{24}{23}\) 

    \(=\left(\frac{37}{53}x\frac{53}{37}\right)x\left(\frac{23}{48}x\frac{24}{23}\right)\)

    \(=1x\frac{24}{48}\)

    \(=1x\frac{1}{2}\)

    \(=\frac{1}{2}\)

37/53 x 23/48 x 535353/373737x242424/232323= 1/5 =0,5

ta có: \(\frac{535353}{373737}=\frac{535353\div10101}{373737\div10101}=\frac{53}{37}\)

và \(\frac{242424}{232323}=\frac{242424\div10101}{232323\div10101}=\frac{24}{23}\)

Vậy \(\frac{37}{53}\times\frac{23}{48}\times\frac{53}{37}\times\frac{24}{23}\)

\(=\frac{37\times23\times53\times24}{53\times48\times37\times23}\)

\(=\frac{24}{48}\)

\(=\frac{1}{2}\)

\(27\cdot\left(\dfrac{373737}{424242}+\dfrac{373737}{565656}+\dfrac{373737}{727272}\right)\\ =27\cdot\left(\dfrac{37}{42}+\dfrac{37}{56}+\dfrac{37}{72}\right)\\ =27\cdot37\cdot\left(\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\right)\\ =999\cdot\left(\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}\right)\\ =999\cdot\left(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)\\ =999\cdot\left(\dfrac{1}{6}-\dfrac{1}{9}\right)\\ =999\cdot\dfrac{1}{18}\\ =\dfrac{111}{2}\)

\(27.\left(\dfrac{373737}{424242}+\dfrac{373737}{565656}+\dfrac{373737}{727272}\right)=\dfrac{111}{2}\)