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a, ( 532 x 7 - 266 x 14 ) x ( 532 x 7 + 266 )
= 3724 - 3714 x 3724 + 266
= 0 x 3990
= 0
b, 117 x ( 36 + 62 ) - 17 x ( 62 + 36 )
= 117 x 98 - 17 x 98
= 11466 - 1666
= 9800
a) = 117 x 100 - 17 x 100
= ( 117 - 17 ) x 100
= 100 x 100
= 10000
b) ( 532 x 7 - 266 x 14 ) x ( 532 x 7 + 266 )
= 532 x 7 - 266 x ( 2 x 7 ) x 3990
= 532 x 7 - 266 x 2 x 7 x 3990
= (532 x 7 - 532 x 7) x 3990
= 0 x 3990
= 0
c) 506 x 5 + 1012 + 253 x 6
= 506 x 5 + (506 x 2) + 253 x ( 2 x 3 )
= 506 x 5 + 506 x 2 + 253 x 2 x 3
= 506 x 5 + 506 x 2 + 506 x 3
= 506 x ( 5 + 2 + 3 )
= 506 x 10
= 5060
a) \(175-\left(-25\right)+62-\left(1200+62\right)\)
\(=\left(175+25\right)+\left(62-62\right)-1200\)
\(=200-1200\)
\(=-1000\)
b) \(\left(-25\right)\cdot8\cdot\left(-4\right)\cdot\left(-125\right)\cdot3\)
\(=3\left[\left(-25\right)\cdot\left(-4\right)\right]\left[\left(-125\right)\cdot8\right]\)
\(=3\cdot100\cdot\left(-1000\right)\)
\(=-300000\)
c) \(27\cdot\left(-17\right)+17\cdot\left(-73\right)\)
\(=27\cdot\left(-17\right)+73\cdot\left(-17\right)\)
\(=\left(-17\right)\cdot\left(27+73\right)\)
\(=\left(-17\right)\cdot100\)
\(=-1700\)
d) \(512\cdot\left(2-128\right)-128\cdot\left(-512\right)\)
\(=512\cdot\left(2-128\right)+128\cdot512\)
\(=512\left(2-128+128\right)\)
\(=512\cdot2\)
\(=1024\)
a, \(A=\dfrac{1}{3}.\dfrac{-6}{-3}.\dfrac{-9}{10}.\dfrac{-13}{36}\)
\(A=\dfrac{1.\left(-6\right).\left(-9\right).\left(-13\right)}{3.13.10.36}\)
\(A=\dfrac{-1}{10.2}\)
\(A=\dfrac{-1}{20}\)
b, \(B=\dfrac{-1}{3}.\dfrac{-15}{17}.\dfrac{34}{45}\)
\(B=\dfrac{\left(-1\right).\left(-15\right).34}{3.17.45}\)
\(B=\dfrac{2}{3.3}\)
\(B=\dfrac{2}{9}\)
c, \(C=\dfrac{1}{3}.\dfrac{4}{5}+\dfrac{1}{3}.\dfrac{6}{5}+\dfrac{2}{3}\)
\(C=\dfrac{1}{3}.\left(\dfrac{4}{5}+\dfrac{6}{5}\right)+\dfrac{2}{3}\)
\(C=\dfrac{1}{3}.2+\dfrac{2}{3}\)
\(C=\dfrac{2}{3}+\dfrac{2}{3}\)
\(C=\dfrac{4}{3}\)
d, \(D=\dfrac{-5}{6}.\dfrac{4}{19}+\dfrac{-7}{12}.\dfrac{4}{19}-\dfrac{40}{57}\)
\(D=\dfrac{4}{19}.\left(\dfrac{-5}{6}+\dfrac{-7}{12}\right)-\dfrac{40}{57}\)
\(D=\dfrac{4}{19}.\dfrac{-17}{12}-\dfrac{40}{57}\)
\(D=\dfrac{-17}{57}-\dfrac{40}{57}\)
\(D=\dfrac{-57}{57}=-1\)
e, \(E=\dfrac{3}{7}.\dfrac{9}{26}-\dfrac{1}{14}.\dfrac{1}{13}-\dfrac{1}{7}\)
\(E=\dfrac{3}{7}.\dfrac{9}{26}-\left(\dfrac{1}{14}.\dfrac{1}{13}+\dfrac{1}{7}\right)\)
\(E=\dfrac{3}{7}.\dfrac{9}{26}-\left(\dfrac{1}{182}+\dfrac{1}{7}\right)\)
\(E=\dfrac{3}{7}.\dfrac{9}{26}-\dfrac{27}{182}\)
\(E=\dfrac{27}{182}-\dfrac{27}{182}\)
\(E=0\)
a, 54 x 113 + 54 x 113 + 113
= 113 x ( 54 + 54 + 1 )
= 113 x 109
= 12 317
b, ( 532 x 7 - 266 x 14 ) x ( 532 x 7 + 266 )
= ( 266 x 2 x 7 - 266 x 14 ) - ( 532 x 7 + 266 )
= 266 x ( 2 x 7 - 14 )
= 266 x ( 14 - 14 )
= 266 x 0
= 0
c, 117 x ( 36 + 62 ) - 17 x ( 62 + 36 )
= 117 x 98 - 17 x 98
= 98 x ( 117 - 17 )
= 98 x 100
= 9800
d, ( 145 x 99 + 145 ) - ( 143 x 101 - 143 )
= 145 x ( 99 + 1 ) - 143 x ( 101 - 1 )
= 145 x 100 - 143 x 100
= 14500 - 14300
= 200
e, 45 x 16 - 17
______________
45 x 15 + 28
Ta có : 45 x 16 - 17
= 720 - 17
= 703
Ta có : 45 x 15 + 28
= 675 + 28
= 703
Vậy 45 x 16 - 17 703
______________ = _____________ = 1
45 x 15 + 28 703
( * giải thích thêm : __________ chính là dấu chia đó )
\(\dfrac{1}{4}.\dfrac{2}{6}.\dfrac{3}{8}.\dfrac{4}{10}.\dfrac{5}{12}.....\dfrac{30}{62}.\dfrac{31}{64}=2x\)
\(\dfrac{1.2.3.4.5.....30.31}{\left(2.2\right)\left(2.3\right)\left(2.4\right)\left(2.5\right)\left(2.6\right).....\left(2.31\right)\left(2.32\right)}=2x\)
\(\dfrac{1\left(2.3.4.5....30.31\right)}{32\left(2.3.4.5.....31\right).2^{31}}=2x\)
\(\dfrac{1}{2^5.2^{31}}=2x\Rightarrow2x=\dfrac{1}{2^{36}}\Rightarrow x=\dfrac{1}{2^{36}}\div2=\dfrac{1}{2^{37}}\)
Vậy x = \(\dfrac{1}{2^{37}}\)
\(\dfrac{1}{4}\cdot\dfrac{2}{6}\cdot\dfrac{3}{8}\cdot\dfrac{4}{10}\cdot...\cdot\dfrac{30}{62}\cdot\dfrac{31}{64}=2x\\ \dfrac{1}{2\cdot2}\cdot\dfrac{2}{2\cdot3}\cdot\dfrac{3}{2\cdot4}\cdot\dfrac{4}{2\cdot5}\cdot...\cdot\dfrac{30}{2\cdot31}\cdot\dfrac{31}{2\cdot32}=2x\\ \dfrac{1}{2}\cdot\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot...\cdot\dfrac{30}{31}\cdot\dfrac{31}{32}\right)=2x\\ \dfrac{1}{2}\cdot\left(\dfrac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{2\cdot3\cdot4\cdot5\cdot...\cdot31\cdot32}\right)=2x\\ \dfrac{1}{2}\cdot\dfrac{1}{32}=2x\\ 2x=\dfrac{1}{64}\\ x=\dfrac{1}{64}:2\\ x=\dfrac{1}{128}\)
\(A\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\\\Leftrightarrow \left(x-1\right)^{x+4}-\left(x-1\right)^{x+2}=0\\ \Leftrightarrow\left(x-1\right)^{x+2}\left(\left(x-1\right)^{x+2}+1\right)=0\\ \Leftrightarrow\left(x-1\right)^{x+2}=0hoac\left(x-1\right)^{x+2}+1=0\)
Giả tiếp đc x=1
