so sánh: 459 và 380
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Ta có: \(\dfrac{-371}{-459}=\dfrac{371}{459}\) là một số dương
=> \(\dfrac{-371}{-459}>\dfrac{-371}{159}\)
`@` `\text {Ans}`
`\downarrow`
`315/380 = 1 - 65/380`
`316/380 = 1 - 65/381`
Mà `65/380 > 65/381`
`-> 1 - 65/380 < 1 - 65/381`
`-> 315/380 < 316/381`
`=> -315/380 > -316/381`
315/380=1-65/380
316/381=1-65/381
mà 65/380>65/381
nên 315/380<316/381
=>-315/380>-316/381
-315/380 = -120015/144780
-316/381 = -120080/144780
Do -120015 > -120080
-120015/144780 > -120080/144780
⇒ -315/380 > -316/381
- Ta thấy 8/6 là phân số lớn hơn 1 vì chúng có tử số lớn hơn mẫu số, còn 42/43 là phân số bé hơn 1 vì chúng có tử số nhỏ hơn mẫu số nên 8/6 > 42/43.
- Ta thấy 405/2001 < 459/1997 vì 405/2001 là phân số có tử số nhỏ hơn phân số 459/1997 và còn phải chia cho mẫu số lớn hơn mẫu số của phân số 459/1997.
Số lớn nhất trong các số 459 495; 459 549; 549 954 và 549 945 là 549 954.
Chọn C.
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\(4^{59}< 4^{60}\)
Ta có:
\(4^{60}=\left(4^3\right)^{20}=64^{20}\)
\(3^{80}=\left(3^4\right)^{20}=81^{20}\)
Mà: \(81>64\)
\(\Rightarrow81^{20}>64^{20}\)
\(\Rightarrow3^{80}>4^{60}\)
\(\Rightarrow3^{80}>4^{59}\)