So sánh A= 30^8+1/30^9+1 với B=30^9+1/30^10+1 Giúp em vs em cần gấp!! 16/08/2021 Bởi Josie So sánh A= 30^8+1/30^9+1 với B=30^9+1/30^10+1 Giúp em vs em cần gấp!!
$ 30 A = \dfrac{30^{9} + 30}{30^9+1} = \dfrac{30^{9} + 1+ 29}{30^9+1} $ $ = \dfrac{30^{9} + 1}{30^9+1} + \dfrac{29}{30^9+1} = 1 + \dfrac{29}{30^9+1} $ $30B = \dfrac{30^{10} + 30}{30^{10}+1} = \dfrac{30^{10} + 1+ 29}{30^{10}+1} $ $ = \dfrac{30^{10} + 1}{30^{10}+1} + \dfrac{29}{30^{10}+1} = 1 + \dfrac{29}{30^{10}+1} $ Ta có $ 30^9 +1 < 30^{10} +1 \to \dfrac{29}{30^9+1} > \dfrac{29}{30^{10}+1} $ $\to 1 + \dfrac{29}{30^9+1} > 1 + \dfrac{29}{30^{10}+1} $ $\to 30A > 30B$ $\to A >B$ Bình luận
Đáp án + Giải thích các bước giải: `A=(30^8+1)/(30^9+1)` `=>30A=(30(30^8+1))/(30^9+1)=(30^9+30)/(30^9+1)=((30^9+1)+29)/(30^9+1)=1 + 29/(30^9+1)` `B=(30^9+1)/(30^10+1)` `=>30B=(30(30^9+1))/(30^10+1)=(30^10+30)/(30^10+1)=((30^10+1)+29)/(30^10+1)=1 + 29/(30^10+1)` Vì `30^10+1>30^9+1` Nên `29/(30^10+1)<29/(30^9+1)` `=>1 + 29/(30^10+1)< 1 + 29/(30^9+1)` `=>30B<30A` Vậy `B<A` Bình luận
$ 30 A = \dfrac{30^{9} + 30}{30^9+1} = \dfrac{30^{9} + 1+ 29}{30^9+1} $
$ = \dfrac{30^{9} + 1}{30^9+1} + \dfrac{29}{30^9+1} = 1 + \dfrac{29}{30^9+1} $
$30B = \dfrac{30^{10} + 30}{30^{10}+1} = \dfrac{30^{10} + 1+ 29}{30^{10}+1} $
$ = \dfrac{30^{10} + 1}{30^{10}+1} + \dfrac{29}{30^{10}+1} = 1 + \dfrac{29}{30^{10}+1} $
Ta có $ 30^9 +1 < 30^{10} +1 \to \dfrac{29}{30^9+1} > \dfrac{29}{30^{10}+1} $
$\to 1 + \dfrac{29}{30^9+1} > 1 + \dfrac{29}{30^{10}+1} $
$\to 30A > 30B$
$\to A >B$
Đáp án + Giải thích các bước giải:
`A=(30^8+1)/(30^9+1)`
`=>30A=(30(30^8+1))/(30^9+1)=(30^9+30)/(30^9+1)=((30^9+1)+29)/(30^9+1)=1 + 29/(30^9+1)`
`B=(30^9+1)/(30^10+1)`
`=>30B=(30(30^9+1))/(30^10+1)=(30^10+30)/(30^10+1)=((30^10+1)+29)/(30^10+1)=1 + 29/(30^10+1)`
Vì `30^10+1>30^9+1`
Nên `29/(30^10+1)<29/(30^9+1)`
`=>1 + 29/(30^10+1)< 1 + 29/(30^9+1)`
`=>30B<30A`
Vậy `B<A`