Thực hiện phép tính: (2¹⁰⁰+2¹⁰¹+2¹⁰²) : (2⁹⁷+2⁹⁸+2⁹⁹)
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1) 5 + (-4) = 1
2) (-8) + 2 = -6
3) 8 + (-2) = 6
4) 11 + (-3) = 8
5) (-11) + 2 = -9
6) (-7) + 3 = -4
7) (-5) + 5 = 0
8) 11 + (-12) = -1
9) (-18) + 20 = 2
10) (15) + (-12) = 3
11) (-17) + 17 = 0
12) 16 + (-2) = 14
13) (30) + (-14) = 16
14) (-19) + 20 = 1
15) (-18) + 15 = -3
16) (10) + (-6) = 4
17) (-28) + 14 = -14
18) 15 + (-30) = -15
19) (15) + (-4) = 11
20) (-21) + 11 = -10
21) 8 + (-22) = -14
22) (-15) + 4 = -11
23) (-3) + 2 = -1
24) 17 + (-14) = 3
25) 17 + (-14) = 3
`@` `\text {Ans}`
`\downarrow`
`(x^2 + 2)^2`
`= x^4 + 4x^2 + 4`
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`@` Áp dụng: `(A+B)^2 = A^2 + 2AB + B^2.`
\(50+2\left(7-2\right)^2\\ =50+2.5^2\\ =50+2.25\\ =50+50\\ =100.\)
\(=\dfrac{3}{2\left(x+3\right)}+\dfrac{6-x}{2x\left(x+3\right)}=\dfrac{3x+6-x}{2x\left(x+3\right)}=\dfrac{2x+6}{2x\left(x+6\right)}=\dfrac{2\left(x+3\right)}{2x\left(x+3\right)}=\dfrac{1}{x}\)
\(=\dfrac{3x+6-x}{2x\left(x+3\right)}=\dfrac{2x+6}{2x\left(x+3\right)}=\dfrac{1}{x}\)
\(S=-\left(1+2+...+2^{2009}+2^{2010}\right)\)
\(-2S=2\left(1+2+...+2^{2009}+2^{2010}\right)\)
\(\Rightarrow-2S+S=-S=2+2^2+...+2^{2010}+2^{2011}-1-2-...-2^{2009}-2^{2010}\)
\(-S=2^{2011}-1\Rightarrow S=1-2^{2011}\)
S=22010 - 22009 - 22008 -...-2-1
=>2S=2 x 22010 - 2 x 22009 - 2 x 22008 -...-2 x 2 -2 x 1
2S=22011 - 22010 - 22009 - ... - 22 -2
=>S=1-22011
Ta có: ( - 2 ) 5 : ( - 2 ) 3 = ( - 2 ) 5 - 3 = ( - 2 ) 2 = 4 .
\(100x^2-49y^2=\left(10x-7y\right)\left(10x+7y\right)\)
Ta có: \(\left(x+3\right)^2+\left(x-3\right)^2+2\left(x^2-9\right)\)
\(=\left(x+3\right)^2+2\cdot\left(x+3\right)\cdot\left(x-3\right)+\left(x-3\right)^2\)
\(=\left(x+3+x-3\right)^2=\left(2x\right)^2=4x^2\)
\(\frac{\left(2^{100}+2^{101}+2^{102}\right)}{\left(2^{97}+2^{98}+2^{99}\right)}=\frac{2^{100}(1+2+2^2)}{2^{97}(1+2+2^2)}=\frac{2^{100}(1+2+4)}{2^{97}(1+2+4)}=\frac{2^{100}\cdot7}{2^{97}\cdot7}=\frac{2^{100}}{2^{97}}=2^{100-97}=2^3=8\)
Ta có: \(\frac{2^{100}+2^{101}+2^{102}}{2^{97}+2^{98}+2^{99}}\)
\(=\frac{2^{100}\left(1+2+2^2\right)}{2^{97}\left(1+2+2^2\right)}=2^3=8\)