cau 1 A=100^100+1 ,B=100^101+1 ———————- —————- 100^99+1 100^100+1 Question cau 1 A=100^100+1 ,B=100^101+1 ———————- —————- 100^99+1 100^100+1 in progress 0 Môn Toán Cherry 2 years 2021-04-22T22:20:05+00:00 2021-04-22T22:20:05+00:00 2 Answers 24 views 0
Answers ( )
Đáp án:
– `A <B`
Giải thích các bước giải:
$\text{B = $\dfrac{100^{101} + 1}{100^{100}}$ + 1 > 1}$
`=>` $\text{B = $\dfrac{100^{101} + 1 + 99}{100^{100} + 1 + 99}$}$
$\text{= $\dfrac{100^{101} + 100}{100^{100} + 100}$}$
$\text{= $\dfrac{(100^{100} + 1) . 100}{(100^{99} + 1) .100}$}$
$\text{= $\dfrac{100^{100} + 1}{100^{99} + 1}$ = A}$
Vậy `A < B`
Đáp án:
. Có: 100101+1100100+1>1⇒100101+1100100+1>100101+(1+99)100100+(1+99)100101+1100100+1>1⇒100101+1100100+1>100101+(1+99)100100+(1+99)
⇒B>100101+100100100+100⇒B>100(100100+1)100(10099+1)⇒B>100100+110099+1=A⇔A<B⇒B>100101+100100100+100⇒B>100(100100+1)100(10099+1)⇒B>100100+110099+1=A⇔A<B
Vậy A < B
b. Có: 1316+11317+1<0⇒1316+11317+1<1316+(1+12)1317+(1+12)1316+11317+1<0⇒1316+11317+1<1316+(1+12)1317+(1+12)
⇒B<1316+131317+13⇒B<13(1315+1)13(1316+1)⇒B<1315+11316+1=A⇔A>B⇒B<1316+131317+13⇒B<13(1315+1)13(1316+1)⇒B<1315+11316+1=A⇔A>B
Vậy A > B
Giải thích các bước giải: