So sánh: a) A= 100^20-1/ 100^21-98 B= 100^19-1/ 100^20-98

0 bình luận về “So sánh: a) A= 100^20-1/ 100^21-98 B= 100^19-1/ 100^20-98”

1. Đáp án:

   `A>B` 

   Giải thích các bước giải:

    Ta có:

   `A=(100^20-1)/(100^21-98)`

   `=(100^20-98/100-2/100)/(100^21-98)`

   `=(1/100(100^21-98)-2/100)/(100^21-98)`

   `=1/100-(2/100)/(100^21-98)`

   Tương tự ta cũng có:

   `B=1/100-(2/100)/(100^20-98)`

   Vì `100^20<100^21`

   `=>100^20-98<100^21-98`

   `=>1/(100^20-98)>1/(100^21-98)`

   `=>(2/100)/(100^20-98)>(2/100)/(100^21-98)`

   `=>1/100-(2/100)/(100^20-98)<1-(2/100)/(100^21-98)`

   Hay`A>B.`

   Trả lời

2. Ta có:

   $A = \dfrac{100^{20} – 1}{100^{21} – 98}$

   $100A = \dfrac{100^{21} – 100}{100^{21} – 98}$

   $100A = \dfrac{100^{21} – 98 -2}{100^{21} – 98}$

   $100A = 1 – \dfrac{2}{100^{21} – 98}$

   $B = \dfrac{100^{19} – 1}{100^{20} – 98}$

   $100B = \dfrac{100^{20} – 100}{100^{20} – 98}$

   $100B = \dfrac{100^{20} – 98 -2}{100^{20} – 98}$

   $100B = 1 – \dfrac{2}{100^{20} – 98}$

   Vì : $\dfrac{2}{100^{21} – 98} < \dfrac{2}{100^{20}-98}$

   $⇒ 100A > 100B$

   $⇒ A > B$

   Trả lời