a.
M=\(\dfrac{1}{5}\) . (\(\dfrac{1}{4}\)-\(\dfrac{1}{9}\)+\(\dfrac{1}{9}\)-\(\dfrac{1}{14}\)+\(\dfrac{1}{14}\) - \(\dfrac{1}{19}\)+...+\(\dfrac{1}{44}\)- \(\dfrac{1}{49}\)) . \(\dfrac{2-\left(1+3+5+7+...+49\right)}{89}\)
M = \(\dfrac{1}{5}\) . (\(\dfrac{1}{4}\)- \(\dfrac{1}{49}\)).\(\dfrac{2-\left(12.50+25\right)}{89}\)
M =\(-\dfrac{5.9.7.89}{5.4.7.7.89}=\dfrac{-9}{28}\)
b.
áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\dfrac{1+3y}{12}=\dfrac{1+5y}{5x}=\dfrac{1+7y}{4x}=\dfrac{1+7y-1-5y}{4x-5x}=\dfrac{2y}{-x}=\dfrac{1+5y-1-3y}{5x-12}=\dfrac{2y}{5x-12}\)=>\(\dfrac{2y}{-x}=\dfrac{2y}{5x-12}\)
=> -x = 5x -12 => x= 2
Thay x= 2 vào trên ta được:
\(\dfrac{1+3y}{12}=\dfrac{2y}{-2}=-y\)
=> 1 = -15y => y= \(\dfrac{-1}{15}\)
Vậy x = 2 và y = \(\dfrac{-1}{5}\)
