Question

a
vio
Q. What are the values
of
x that satisfy the equation
|x 0 2
​

Answer 1

${\pmb{\underline{\sf{Required \: Solution....}}}}$

$\left| \begin{array}{cc} x & 0&2 \\2x & 2&1 \\ 1&1&1\end{array} \right| + \left| \begin{array}{cc} 3x & 0&2 \\x {}^{2} & 2&1 \\ 0&1&1\end{array} \right| = 0$

$\sf\colorbox{green}{see \: first \: determinants \: along \: 1st \: row \: in \: both \: .. }$

Let's Start ⭐:

$: \implies \: x(2 - 1) + 2(2x - 2) + 3x(2 - 1) + 2(x {}^{2} ) = 0 \\ : \implies4x + 4x - 4 + 2x {}^{2} = 0 \\ : \implies x {}^{2} + 4x - 2 = 0$

Find Roots : -

$\: \implies \: x = \frac{ - 4± \sqrt{16 + 8} }{2} \\ \implies \: x = \frac{ - 4±2 \sqrt{6} }{2} \\ \boxed{x = - 2± \sqrt{6} }$

• x = - 2 +√6
• x= - 2 - √6

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$\blue{hope \: this \: helps \: you!! \: }$

@Mahor2111

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