Question

Determine x tal que:
$\left[\begin{array}{ccc}2x&x-2&\\4x + 5&3x-1\end{array}\right] = 11$

Answer 1

Determinante da matriz 2x2:

$\left(2x\cdot \left(3x-1\right)\right)-\left(\left(x-2\right)\cdot \left(4x+5\right)\right)=11\\6x^2-2x-\left(4x^2+5x-8x-10\right)=11\\6x^2-2x-4x^2-5x+8x+10=11\\2x^2+x+10=11\\2x^2+x+10-11=0\\2x^2+x-1=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\x=\frac{-1\pm \sqrt{1^2-4\cdot 2\cdot \left(-1\right)}}{2\cdot 1}\\x=\frac{-1\pm \sqrt{1+8}}{2}\\x=\frac{-1\pm \sqrt{9}}{2}\\x=\frac{-1\pm 3}{2}\\\\x1=\frac{-1+3}{2}\\x1=\frac{2}{2}\\x1=1\\\\x2=\frac{-1-3}{2}\\x2=-\frac{4}{2}\\x2=-2$

→ Solução do problema:

$\boxed{\bold{S=\left\{1,-2\right\}}}$