Tìm giá trị y thỏa mãn 49(y – 4)² – 9(y + 2)² = 0.

A. \(\left[ \begin{array}{l}y = \frac{{11}}{5}\\y = \frac{{17}}{2}\end{array} \right.\);

B. \(\left[ \begin{array}{l}y = \frac{{ - 11}}{5}\\y = 6\end{array} \right.\);

C. \(\left[ \begin{array}{l}y = \frac{{11}}{5}\\y = - 6\end{array} \right.\);

D. \(\left[ \begin{array}{l}y = \frac{{ - 11}}{5}\\y = - \frac{{17}}{2}\end{array} \right.\).

Đáp án đúng là: A

Ta có 49(y – 4)² − 9(y + 2)²  = 0

⇔ 49(y² − 8y + 16) − (y² + 4y + 4) = 0

⇔ 49y² − 392y + 784 – 9y² − 36y − 36 = 0

⇔ 40y² − 428y + 748 = 0 

⇔ 4(y² − 107y + 187) = 0

⇔ 4[(10y² − 22y) − ( 85y − 187)] = 0 

⇔ 4[2y(5y − 11) − 17(5y − 11)] = 0

⇔ 4(5y − 11)(2y − 17) = 0

\( \Leftrightarrow \left[ \begin{array}{l}5y - 11 = 0\\2y - 17 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}y = \frac{{11}}{5}\\y = \frac{{17}}{2}\end{array} \right.\)