Question

x के मान ज्ञात कीजिए यदि ${\displaystyle \left|\begin{array}{cc}2& 4\\ 5& 1\end{array}\right|=\left|\begin{array}{cc}2x& 4\\ 6& x\end{array}\right|}$

Answer 1

${\displaystyle \left|\begin{array}{cc}2& 4\\ 5& 1\end{array}\right|=\left|\begin{array}{cc}2x& 4\\ 6& x\end{array}\right|}$

⇒ ${\displaystyle 2\left(1\right)-5\left(4\right)=2x\left(x\right)-24}$

⇒  ${\displaystyle 2-20=2x^2-24}$

⇒ ${\displaystyle -18=2x^2-24}$

⇒  ${\displaystyle 2x^2-24+18=18}$

⇒  ${\displaystyle 2x^2-6=0}$

⇒  ${\displaystyle x^2=\frac{6}{2}=3}$

⇒  ${\displaystyle x=\pm \sqrt{3}}$