यदि |(4 1),(2 1)|^2 = |(3 2),(1 x)|-|(x 3),(-2 1)| हो तो x का मान है

Question

यदि  \(\begin{vmatrix}4&1\\ 2&1\end{vmatrix}^2\) = \(\begin{vmatrix}3&2\\ 1&x\end{vmatrix}\)- \(\begin{vmatrix}x&3\\ -2&1\end{vmatrix}\) हो तो x का मान है

(a) 6

(b) 8

(c) 7

(d) 0

Answer 1

(a)  \(\begin{vmatrix}4&1\\ 2&1\end{vmatrix}^2\) = \(\begin{vmatrix}3&2\\ 1&x\end{vmatrix}\)- \(\begin{vmatrix}x&3\\ -2&1\end{vmatrix}\) 

⇒ (4 – 2)² = (3x – 2) – (x + 6)

⇒ (2)² = 3x – 2 – x – 6

⇒ 4 = 2x – 8

⇒ 4 + 8 = 2x

अत: x = 6