Question

tìm x biết

( x-1) + ( x-2) + (x-3) +....+ (x-100) = 4950

Answer 1

\(\left(x-1\right)+\left(x-2\right)+\left(x-3\right)+...+\left(x-100\right)=4950\\ \Leftrightarrow100x-\left(1+2+3+...+100\right)=4950\\ \Leftrightarrow100x-\frac{\left(100+1\right)100}{2}=4950\\ \Leftrightarrow100x-5050=4950\\ \Rightarrow100x=-100\\ \Rightarrow x=-1\)

Answer 2

tìm x biết

( x-1) + ( x-2) + (x-3) +....+ (x-100) = 4950

⇔\(\left(x+x+x+....+x\right)-\left(1+2+3+....+100\right)=4950\)

⇔\(\left(x.100\right)-\left(1+100\right).100:2=4950\)

⇔\(\left(x.100\right)-5050=4950\)

⇔\(100x=4950+5050\)

⇔\(100x=10000\)

⇔ \(x=100\)