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124 + (2012 - 2 . x) = 300

(2012 - 2 . x) = 300 - 124

(2012 - 2 . x) = 176

2 . x = 2012 - 176

2 . x = 1836

x = 1836 : 2

x = 918.

918

1538

1538

\(A=1.2.3+2.3.4+3.4.5+...+99.100.101\)

\(\Rightarrow4A=1.2.3.4+2.3.4.4+99.100.101.4\)

\(\Rightarrow4A=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+...+99.100.101.\left(102-98\right)\)

\(\Rightarrow4A=\left(1.2.3.4+2.3.4.5+...+99.100+101.102\right)-\left(0.1.2.3+1.2.3.4+...+98.99.100.101\right)\)

\(\Rightarrow4A=99.100.101.102-0.1.2.3\)

\(\Rightarrow A=\dfrac{99.100.101.102-0.1.2.3}{4}\)

\(B=1.3.5+3.5.7+5.7.9+...+95.97.99\)

\(\Rightarrow8B=1.3.5.8+3.5.7.8+5.7.9.8+...+95.97.99.8\)

\(\Rightarrow8B=1.3.5.\left(7+1\right)+3.5.7.\left(9-1\right)+5.7.9.\left(11-3\right)+...+95.97.99.\left(101-93\right)\)

\(\Rightarrow8B=1.3.5.7+1.1.3.5+3.5.7.9-1.3.5.7+5.7.9.11-3.5.7.9+...+95.97.99.101-93.95.97.99\)

\(\Rightarrow8B=1.1.3.5+95.97.99.101\)

\(\Rightarrow B=\dfrac{1.1.3.5+95.97.99.101}{8}\)

B= 912720

`27 . 64 + 27 .33 + 3 . 27`

`=27 . (64 + 33 + 3)`

`=27. 100`

`=2700`

\(27.64+27.33+3.27\)

\(=27.\left(64+33+3\right)\)

\(=27.100\)

\(=2700\)

a) 67.101-67 = 6767-67 = 6700

b) 358.96+358.4 = 358 .( 96+4) = 358.100 = 35800

c) 2022.138-2022.38 = 2022. ( 138-38) = 2022.100 = 202200

d) 125.72 = 9000

e) 2030.101 = 205030

f) 2021.99 = 200079

x=9

`2^x = 512`

`2^x = 2^9`

`=> x = 9`

x² = 9

x² = 3²

x =3

3