cho a+45 ,b=204,c=126 tìm uoc chung lon nhat (a,b,c)
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291 và 536
291= (25)18.2 = 3218.2
536 = (52)18 = 2518
32 > 25 ⇒ 3218 > 2518 ⇒ 291 > 536
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\(2^{91}>2^{90}\)
Ta có:
\(2^{90}=\left(2^5\right)^{18}=32^{18}\)
\(5^{36}=\left(5^2\right)^{18}=25^{18}\)
Mà: \(32>25\)
\(\Rightarrow32^{18}>25^{18}\)
\(\Rightarrow2^{90}>5^{36}\)
\(\Rightarrow2^{91}>5^{36}\)
Ta có:
\(2^{91}>2^{90}=\left(2^5\right)^{18}=32^{18}>25^{18}=\left(5^2\right)^{18}=5^{2.18}=5^{36}\)
Vậy \(2^{91}>5^{36}\).
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\(x\)(y - 3) = -12
⇒ \(x\).(3-y) = 12
12 = 22.3
Ư(12) = {-12; -6; -3; -4; -2; -1; 1; 2; 3; 4;6;12}
Lập bảng ta có:
3 - y | -12 | -6 | -4 | -3 | -2 | -1 | 1 | 2 | 3 | 4 | 6 | 12 |
y | 15 | 9 | 7 | 6 | 5 | 4 | 2 | 1 | 0 | -1 | -3 | -9 |
\(x\) | -1 | -2 | -3 | -4 | -6 | -12 | 12 | 6 | 4 | 3 | 2 | 1 |
(\(x;y\)) | (-1;15) | (-2;9) | (-3;7) | (-4;6) | (-6;5) | (-12;4) | (12;2) | (6;1) | (4;0) | (3;-1) | (2;-3) | (12;-9) |
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Lời giải:
$199^{20}< 200^{20}=100^{20}.2^{20}=100^{20}.(2^5)^4=100^{20}.32^4$
$< 100^{20}.100^4=100^{24}$
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\(3^{151}< 3^{150}\)
Ta có:
\(3^{150}=\left(3^2\right)^{75}=9^{75}\)
\(2^{225}=\left(2^3\right)^{75}=8^{75}\)
Mà: \(9>8\)
\(\Rightarrow9^{75}>8^{75}\)
\(\Rightarrow3^{150}>2^{225}\)
\(\Rightarrow3^{151}>2^{225}\)
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Ta có:
\(15^{12}=\left(3\cdot5\right)^{12}=3^{12}\cdot5^{12}\)
\(81^3\cdot125^5=\left(3^4\right)^3\cdot\left(5^3\right)^5=3^{12}\cdot5^{15}\)
Mà: \(15>12\)
\(\Rightarrow5^{15}>5^{12}\)
\(\Rightarrow3^{12}\cdot5^{15}>3^{12}\cdot5^{12}\)
\(\Rightarrow81^3\cdot125^5>15^{12}\)
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Ta có:
\(2^{16}=2^3\cdot2^{13}=8\cdot2^{13}\)
Mà:
\(7< 8\)
\(\Rightarrow7\cdot2^{13}< 8\cdot2^{13}\)
\(\Rightarrow7\cdot2^{13}< 2^{16}\)
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Ta có:
\(a=40=2^3\cdot5\)
\(b=75=5^2\cdot3\)
\(c=105=5\cdot3\cdot7\)
\(\RightarrowƯCLN\left(a,b,c\right)=5\)
\(\Rightarrow BCNN\left(a,b,c\right)=5^2\cdot2^3\cdot3\cdot7=4200\)
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Ta có:
\(5^{23}=5\cdot5^{22}\)
Mà:
\(6>5\)
\(\Rightarrow6\cdot5^{22}>5\cdot5^{22}\)
\(\Rightarrow6\cdot5^{22}>5^{23}\)
Ta có:
\(a=45=3^2\cdot5\)
\(b=204=2^2\cdot3\cdot17\)
\(b=2\cdot3^2\cdot7\)
\(\Rightarrow\text{Ư}CLN\left(a,b,c\right)=3\)
a=45; b= 204; c=126. Tìm ƯCLN(a,b,c)
Ta có: 45 = 32. 5; 204 = 22 .3. 17; 126 = 2 . 32 .7
Thừa số nguyên tố chung là: 3
=> ƯCLN(a,b,c) = ƯCLN(45,204;126) = 3
Vậy ƯCLN(a,b,c) = 3