Question

a,Tính M= \(-\dfrac{4}{1.5}-\dfrac{4}{5.9}-..........-\dfrac{4}{\left(n+4\right).n}\)

b, Tìm x biết:

-4x ( x-5)-2x(8-2x)=-3

Answer 1

\(M=-\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+...+\dfrac{4}{n\left(n+4\right)}\right)\\ =-\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{n}-\dfrac{1}{n+4}\right)\\ =-\left(1-\dfrac{1}{n+4}\right)\\ =-\left(\dfrac{n+3}{n+4}\right)\)

Answer 2

\(-4x\left(x-5\right)-2x\left(8-2x\right)=-3\\ \Rightarrow-4x^2+20x-16x+4x^2=-3\\ \Rightarrow4x=-3\\ \Rightarrow x=-\dfrac{3}{4}\)

Answer 3

a) \(M=-\dfrac{4}{1.5}-\dfrac{4}{5.9}-...-\dfrac{4}{\left(n-4\right)n}\)

⇔ \(M=-\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+...+\dfrac{4}{\left(n-4\right)n}\right)\)

⇔ \(M=-\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{n-4}-\dfrac{1}{n}\right)\)

⇔ \(M=-\left(1-\dfrac{1}{n}\right)\)

⇔ \(M=-\dfrac{n-1}{n}\)

b) - 4x(x - 5) - 2x(8 - 2x) = -3

⇔ -4x² + 20x - 16x + 4x² = -3

⇔ 4x = -3

⇔ x = \(-\dfrac{3}{4}\)