Cho \(A=\dfrac{\dfrac{-5}{8}.\dfrac{3}{7}+\dfrac{3}{7}.\dfrac{3}{4}+\dfrac{1}{7}.\dfrac{1}{2}+\dfrac{15}{8}}{a+\dfrac{5}{6}-\left(\dfrac{-1}{3}\right)}\)
a) Rút gọn A?
b) Tính A khi a=75%
c) Tìm a để A=50%
d) Tìm a thuộc Z để A là số nguyên.
e) Với a = bao nhiêu để A có giá trị bằng với giá trị của biểu thức:
\(B=\dfrac{\dfrac{2}{3}.\dfrac{15}{6}+\left(-0,5\right)^3}{\dfrac{1}{9}.6^2-5\dfrac{1}{3}}\)
Giải
a, Ta có:
\(A=\dfrac{\dfrac{-5}{8}.\dfrac{3}{7}+\dfrac{3}{7}.\dfrac{3}{4}+\dfrac{3}{7}.\dfrac{1}{6}+\dfrac{1}{8}.15}{a+\dfrac{5}{6}+\dfrac{1}{3}}\)
\(A=\dfrac{\dfrac{3}{7}.\left(\dfrac{-5}{8}+\dfrac{3}{4}+\dfrac{1}{6}\right)+\dfrac{1}{8}.15}{a+\dfrac{7}{6}}\)
\(A=\dfrac{\dfrac{3}{7}.\dfrac{7}{24}+\dfrac{1}{8}.15}{a+\dfrac{7}{6}}\)
\(A=\dfrac{\dfrac{1}{8}+\dfrac{1}{8}.15}{a+\dfrac{7}{6}}\)
\(A=\dfrac{\dfrac{1}{8}.\left(15+1\right)}{a+\dfrac{7}{6}}\)
\(A=\dfrac{2}{a+\dfrac{7}{6}}\)
b, Thay \(a=75\%\) vào \(A\), ta được:
\(A=\dfrac{2}{75\%+\dfrac{7}{6}}\)
\(A=\dfrac{2}{\dfrac{3}{4}+\dfrac{7}{6}}\)
\(\Rightarrow A=\dfrac{23}{12}\)
c, Ta có: \(\dfrac{2}{a+\dfrac{7}{6}}=50\%\)
\(\dfrac{2}{a+\dfrac{7}{6}}=\dfrac{1}{2}\)
\(\dfrac{2}{a+\dfrac{7}{6}}=\dfrac{2}{4}\)
\(\Rightarrow a+\dfrac{7}{6}=4\)
\(\Rightarrow a=\dfrac{17}{6}\)
d, Để \(A\in Z\Rightarrow2⋮a+\dfrac{7}{6}\)
\(\Rightarrow a+\dfrac{7}{6}\in\left\{\pm1;\pm2\right\}\)
\(\circledast,a+\dfrac{7}{6}=1\Rightarrow a=\dfrac{-1}{6}\)
\(\circledast,a+\dfrac{7}{6}=-1\Rightarrow a=\dfrac{-13}{6}\)
\(\circledast,a+\dfrac{7}{6}=2+\Rightarrow a=\dfrac{5}{6}\)
\(\circledast,a+\dfrac{7}{6}=-2\Rightarrow a=\dfrac{-19}{6}\)
\(a\in\varnothing\) khi \(A\in Z\)
e, Ta có:
\(B=\dfrac{5}{3}+\dfrac{-1}{8}\Rightarrow B=\dfrac{37}{24}\)
\(\Rightarrow\dfrac{2}{a+\dfrac{7}{6}}=\dfrac{37}{24}\)
\(a+\dfrac{7}{6}=\dfrac{37}{24}.2\)
\(a+\dfrac{7}{6}=\dfrac{37}{12}\)
\(\Rightarrow a=\dfrac{23}{12}\)
Chúc bạn học thiệt giỏi nha!!!
