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c)
Có Q = P.(x+1) = \(\frac{-3.\left(x+1\right)}{\sqrt{x}-2}\)
\(\Leftrightarrow-Q=\frac{3x+3}{\sqrt{x}-2}=\frac{3x-6\sqrt{x}+6\sqrt{x}+3}{\sqrt{x}-2}=\frac{3\sqrt{x}\left(\sqrt{x}-2\right)+6\left(\sqrt{x}-2\right)+15}{\sqrt{x}-2}\)
\(\Leftrightarrow-Q=3\sqrt{x}+6+\frac{15}{\sqrt{x}-2}\)
\(\Leftrightarrow-Q=3\left(\sqrt{x}-2\right)+\frac{15}{\sqrt{x}-2}+12\)
\(\Leftrightarrow-Q\ge2\sqrt{3\left(\sqrt{x}-2\right).\frac{15}{\sqrt{x}-2}}+12=2\sqrt{45}+12\)
\(\Leftrightarrow-Q\ge6\sqrt{5}+12\)
\(\Leftrightarrow Q\le-6\sqrt{5}-12\)
Dấu " = " Xảy ra khi :
\(3.\left(\sqrt{x}-2\right)=\frac{15}{\sqrt{x}-2}\Leftrightarrow\left(\sqrt{x}-2\right)^2=5\)
\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x}-2=\sqrt{5}\\\sqrt{x}-2=-\sqrt{5}\end{cases}\Leftrightarrow\orbr{\begin{cases}\sqrt{x}=2+\sqrt{5}\Leftrightarrow x=9+4\sqrt{5}\\\sqrt{x}=2-\sqrt{5}\left(Sai\right)\end{cases}}}\)
Vậy Max Q = \(-6\sqrt{5}-12\)khi x = \(9+4\sqrt{5}\)
a ) 9^7 . 9^8 = 97+8 =915
b ) 8^6 : 8^4 = 86-4 = 82
c ) 5^3 . 8^3 = ( 5.8 )3 = 40^3
d ) 24^5 : 6^5 = ( 24:6 )5 = 4^5
a) \(2^5\cdot8^4\\ =2^5\cdot\left(2^3\right)^4\\ =2^5\cdot2^{12}\\ =2^{17}\)
b) \(25^6\cdot125^3\\ =\left(5^2\right)^6\cdot\left(5^3\right)^3\\ =5^{12}\cdot5^9\\ =5^{21}\)
c) \(625^3:25^7\\ =\left(5^4\right)^3:\left(5^2\right)^7\\ =5^{12}:5^{14}\\ =5^{-2}=\frac{1}{5^2}\)
d) \(4^{10}\cdot2^{30}\\ =\left(2^2\right)^{10}\cdot2^{30}\\ =2^{20}\cdot2^{30}\\= 2^{50}\)
e) \(9^{25}\cdot27^4\cdot81^3\\ =\left(3^2\right)^{25}\cdot\left(3^3\right)^4\cdot\left(3^4\right)^3\\ =3^{50}\cdot3^{12}\cdot3^{12}\\ =3^{74}\)
a)\(2.2.2.3.3=2^3.3^2\)
b)\(8.8.8.2=2^3.2^3.2^3.2=2^{10}\)
c)\(8^4.16^5=\left(2^3\right)^4.\left(2^4\right)^5=2^{12}.2^{20}=2^{32}\)
d)\(5^{40}.125^2.625^3=5^{40}.\left(5^3\right)^2.\left(5^4\right)^3=5^{40}.5^6.5^{12}=5^{58}\)
e)\(27^4.81^{10}=\left(3^3\right)^4.\left(3^4\right)^{10}=3^{12}.3^{40}=3^{52}\)
f)\(10^3.100^5.1000^4=10^3.\left(10^2\right)^5.\left(10^3\right)^4=10^3.10^{10}.10^{12}=10^{25}\)
a,\(\left(25^{11}.5^9\right):\left(5^{46}.625\right)\)
\(=\left(5^{42}.5^9\right):\left(5^{46}.5^4\right)\)
\(=5^{51}:5^{50}=5\)
b,\(\left(3^{2011}+3^{2009}\right):3^{2000}:9^4\)
\(=\left(3^{2009}.\left(3^2+1\right)\right):3^{2000}:3^8\)
\(=3^{2009}.10:3^{2008}\)
\(=3.10=30\)
a ) 213. 45 . 82
= 213. ( 22 )5 . ( 23 )2
= 213. 210 . 26
= 229
b ) 369 : 189
= ( 36 : 18 )9
= 29
c ) 1006 . 10004 . 100003
= ( 102 )6 . ( 103 )4 . ( 104 )3
= 1012 . 1012 . 1012
= 1036
d ) 245 : 65 . 88
= ( 24 : 6 )5 . ( 23 )8
= 45 . 224
= ( 22 )5 . 224
= 210 . 224
= 234
a,đổi 45 thành 210
đổi 82 thành 26
ta có 210.26.213 và bằng 229
b,đổi 369 thành 1818
ta có 1818:189 và bằng 189
c,đổi 10004 thành 10040
đổi 100003 thành 100300
ta có 1006.10040.100300 bằng 100346
d,cũng làm theo cách đó và d=1310722
(32)25.(33)4.(34)3=350.312.312=374
(52)50.(53)5=5115
(416)3.48.(42)4=
a 350 x312 x 312 = 374
b 5100 x 515 =5115
c 49 x 48 x 48 = 425
a. 84.165 = (23)4. (24)5 = 212. 220= 232
b. 540.1252.6253= 540. (53)2.(54)3= 540.56.512= 558
c. 274.8110= (33)4.(34)10= 312.340= 352
d. 103 . 1005 .10004= 103. (102)5.(103)4= 103.1010.1012= 1025
a, 815 . 274 = ( 34 )5 . ( 33 )4 = 320 . 312 = 332
b, 6253 : 1252 = ( 54 )3 : ( 53 )2 = 512 : 56 = 56
c, 1824 . 336 = ( 2 . 32 )24 . 336 = 224 . 348 . 336 = 224 . 384
d, 1021 : 514 = ( 2 . 5 )21 : 514 = 221 . 521 : 514 = 221 . 57