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Determinants — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDeterminants2 Marks
Question
If $\begin{vmatrix}2\text{x}&\text{x}+3\\2(\text{x}+1)&\text{x}+1\end{vmatrix}=\begin{vmatrix}1&5\\3&3\end{vmatrix},$ then write the value of x.
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Answer

$\begin{vmatrix}2\text{x}&\text{x}+3\\2(\text{x}+1)&\text{x}+1\end{vmatrix}=\begin{vmatrix}1&5\\3&3\end{vmatrix}$
⇒ (2x)(x + 1) - 2(x + 1)(x + 3) = 13 - 15
⇒ (x + 1)(2x - 2x - 6) = -12
⇒ -6x - 6 = -12
⇒ -6x = -6
⇒ x = 1
Hence, the value of x is 1.

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