Question

3+6+9+......+x=630

 

Answer 1

                                                           Bài giải

\(3+6+9+...+x=630\)

\(\frac{\left[\left(x-3\right)\text{ : }3+1\right]\left(x+3\right)}{2}=630\)

\(\left[\left(x-3\right)\text{ : }3+1\right]\left(x+3\right)=1260\)

\(\left[\frac{x}{3}-1+1\right]\left(x+3\right)=1260\)

\(\frac{x}{3}\left(x+3\right)=1260\)

\(\frac{x^2}{3}+x=1260\)

\(x\left(\frac{x}{3}+1\right)=1260\)

Answer 2

Ta có 3 + 6 + 9 + ... + x = 630

=> [(x - 3) : 3 + 1].(x + 3) : 2 = 630

<=> \(\left(\frac{x-3}{3}+1\right)\left(x+3\right):2=630\)

=> \(\left(\frac{x}{3}-1+1\right)\left(x+3\right)=1260\)

=> \(\frac{x}{3}.\left(x+3\right)=1260\)

=> x(x + 3) = 3780

=> x² + 3x = 3780

=> x² + 3x - 3780 = 0

=> x² + 63x - 60x - 3780 = 0

=> x(x + 63) - 60(x + 63) = 0

=> (x - 60)(x + 63) = 0

=> \(\orbr{\begin{cases}x-60=0\\x+63=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=60\\x=-63\end{cases}}\)

=> x = 60 (Vì trong dãy không có số âm)

Vậy x = 60 là giá trị cần tìm