Tìm giá trị y thỏa mãn 49(y – 4)^2 – 9(y + 2)^2 = 0 A. y = 11/5 hoặc y = 17/2 B. y = -11/5
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08/05/2024
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. \(\left[ \begin{array}{l}y = \frac{{ - 11}}{5}\\y = - \frac{{17}}{2}\end{array} \right.\).
Trả lời
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
\( \Leftrightarrow \left[ \begin{array}{l}5y - 11 = 0\\2y - 17 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}y = \frac{{11}}{5}\\y = \frac{{17}}{2}\end{array} \right.\)
