Tính biểu thức sau A= 2x + 2xy – y với | x | = 2,5; y = -3/4 Tính 3/2.3+3/3.4+3/4.5+….+3/19.20

0 bình luận về “Tính biểu thức sau A= 2x + 2xy – y với | x | = 2,5; y = -3/4 Tính 3/2.3+3/3.4+3/4.5+….+3/19.20”

1. Đáp án:

    $
   A\left ( \dfrac{5}{2};\dfrac{-3}{4} \right )=2\\
   A\left ( \dfrac{-5}{2};\dfrac{-3}{4} \right )=\dfrac{-1}{2}\\
   B=\dfrac{27}{20}$

   Giải thích các bước giải:

    $|x|=2,5\Rightarrow x=\pm \dfrac{5}{2},y=\dfrac{-3}{4}\\
   A\left ( \dfrac{5}{2};\dfrac{-3}{4} \right )=2x+2xy-y=2.\dfrac{5}{2}+2.\dfrac{5}{2}.\dfrac{-3}{4}-\dfrac{-3}{4}\\
   =5+5.\dfrac{-3}{4}+\dfrac{3}{4}\\
   =5-\dfrac{15}{4}+\dfrac{3}{4}\\
   =5-\dfrac{12}{4}\\
   =5-3\\
   =2\\
   A\left ( \dfrac{-5}{2};\dfrac{-3}{4} \right )=2x+2xy-y=2.\dfrac{-5}{2}+2.\dfrac{-5}{2}.\dfrac{-3}{4}-\dfrac{-3}{4}\\
   =-5+5.\dfrac{3}{4}+\dfrac{3}{4}\\
   =-5+\dfrac{15}{4}+\dfrac{3}{4}\\
   =-5+\dfrac{18}{4}\\
   =\dfrac{-20}{4}+\dfrac{18}{4}\\
   =\dfrac{-2}{4}\\
   =\dfrac{-1}{2}\\
   B=\dfrac{3}{2.3}+\dfrac{3}{3.4}+\dfrac{3}{4.5}+…+\dfrac{3}{19.20}\\
   =3.\left (  \dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+…+\dfrac{1}{19.20}\right )\\
   =3.\left ( \dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+…+\dfrac{1}{19}-\dfrac{1}{20} \right )\\
   =3.\left ( \dfrac{1}{2}-\dfrac{1}{20} \right )\\
   =3.\left ( \dfrac{10}{20}-\dfrac{1}{20} \right )\\
   =3.\dfrac{9}{20}\\
   =\dfrac{27}{20}$

   Bình luận