Question

\(\dfrac{x-2}{5}=\dfrac{x}{3}\)

B = 1+2+2²+2³+..........+2²⁰¹⁷

^{\(\dfrac{x+23}{x+40}=\dfrac{3}{4}\)}

Answer 1

\(\dfrac{x-2}{5}=\dfrac{x}{3}\)

\(\Leftrightarrow\left(x-2\right)3=5x\)

\(\Leftrightarrow3x-6=5x\)

\(\Leftrightarrow5x-3x=-6\)

\(\Leftrightarrow2x=-6\)

\(\Leftrightarrow x=-3\)

Vậy .....

b, \(B=1+2+2^2+..........+2^{2017}\)

\(\Leftrightarrow2B=2+2^2+.......+2^{2018}\)

\(\Leftrightarrow2B-B=\left(2+2^2+......+2^{2018}\right)-\left(1+2+......+2^{2017}\right)\)

\(\Leftrightarrow B=2^{2018}-1\)

c, \(\dfrac{x+23}{x+40}=\dfrac{3}{4}\)

\(\Leftrightarrow4\left(x+23\right)=3\left(x+40\right)\)

\(\Leftrightarrow4x+92=3x+120\)

\(\Leftrightarrow4x-3x=120-92\)

\(\Leftrightarrow x=28\)