Question

2 + 4 + 6 + ... + 2x = 9900

2 + 4 + 6 + ... + 2x = 2550

Answer 1

\(a,2+4+6+...+2x=9900\)

\(\Leftrightarrow\dfrac{2+2x}{2}:\left(\dfrac{2-2x}{2}+1\right)=9900\)

\(\Leftrightarrow\left(x+1\right).x=9900\)

\(\Leftrightarrow x^2+x=9900\)

\(\Leftrightarrow x=99\)

\(b,2+4+6+...+2x=2550\)

\(\Leftrightarrow\dfrac{2+2x}{2}:\left(\dfrac{2-2x}{2}+1\right)=2550\)

\(\Leftrightarrow\left(x+1\right).x=2550\)

\(\Leftrightarrow x^2+x=2550\)

\(\Leftrightarrow x=50\)