Tháng Ba 3, 2024

Tìm \(x\) biết: \(a)\left( {x + 2} \right)\left( {x + 3} \right) – \left( {x – 2} \right)\left( {x + 5} \right) = 6\) \(b)\left( {3x + 2} \right)\left( {2x + 9} \right) – \left( {x + 2} \right)\left( {6x + 1} \right) = \left( {x + 1} \right) – \left( {x + 6} \right)\)

Tìm \(x\) biết:

\(a)\left( {x + 2} \right)\left( {x + 3} \right) – \left( {x – 2} \right)\left( {x + 5} \right) = 6\)

\(b)\left( {3x + 2} \right)\left( {2x + 9} \right) – \left( {x + 2} \right)\left( {6x + 1} \right) = \left( {x + 1} \right) – \left( {x + 6} \right)\)

A. \(a) x = 5 \)

\(b) x = \frac{{ – 7}}{6}\)

B. \(a) x = – 5 \)

\(b) x = \frac{{ 7}}{6}\)

C. \(a) x = – 5 \)

\(b) x = \frac{{ – 7}}{6}\)

D. \(a) x = 5 \)

\(b) x = \frac{{ 7}}{6}\)

Hướng dẫn Chọn đáp án là: C

Lời giải chi tiết:

Hướng dẫn giải chi tiết

\(\begin{array}{l}a)\left( {x + 2} \right)(x + 3) – \left( {x – 2} \right)\left( {x + 5} \right) = 6\\ \Leftrightarrow x.x + 3.x + 2.x + 2.3 – x.x – 5.x + 2.x + 2.5 = 6\\ \Leftrightarrow {x^2} + 3x + 2x + 6 – {x^2} – 5x + 2x + 10 = 6\\ \Leftrightarrow 2x + 16 = 6\\ \Leftrightarrow 2x = – 10\\ \Leftrightarrow x = – 5\end{array}\)

\(\begin{array}{l}b)\left( {3x + 2} \right)\left( {2x + 9} \right) – \left( {x + 2} \right)\left( {6x + 1} \right) = (x + 1) – (x + 6)\\ \Leftrightarrow 3x.2x + 9.3x + 2.2x + 2.9 – x.6x – x.1 – 2.6x – 2.1 = x + 1 – x – 6\\ \Leftrightarrow 6{x^2} + 27x + 4x + 18 – 6{x^2} – x – 12x – 2 = – 5\\ \Leftrightarrow 18x + 16 = – 5\\ \Leftrightarrow 18x = – 21\\ \Leftrightarrow x = \frac{{ – 7}}{6}\end{array}\)

Chọn C.