Câu hỏi của Lục Hạ Vy

Question

Biết 1²+ 2²+ 3²+....8²+ 9² = 285. Tính 3² + 6² + 9² +.......24² + 27²

Nguyễn Việt Lâm · Accepted Answer

$1^2+2^2+3^2+...+9^2=285$

$\Leftrightarrow\left(1^2+2^2+3^2+...+8^2+9^2\right).3^2=285.3^2$

$\Leftrightarrow1^2.3^2+2^2.3^2+3^2.3^2+...+8^2.3^2+9^2.3^2=285.9$

$\Leftrightarrow\left(1.3\right)^2+\left(2.3\right)^2+\left(3.3\right)^2+...+\left(8.3\right)^2+\left(9.3\right)^2=2565$

$\Leftrightarrow3^2+6^2+9^2+...+24^2+27^2=2565$

Câu trả lời:

$1^2+2^2+3^2+...+9^2=285$

$\Leftrightarrow\left(1^2+2^2+3^2+...+8^2+9^2\right).3^2=285.3^2$

$\Leftrightarrow1^2.3^2+2^2.3^2+3^2.3^2+...+8^2.3^2+9^2.3^2=285.9$

$\Leftrightarrow\left(1.3\right)^2+\left(2.3\right)^2+\left(3.3\right)^2+...+\left(8.3\right)^2+\left(9.3\right)^2=2565$

$\Leftrightarrow3^2+6^2+9^2+...+24^2+27^2=2565$