Question

3. Soluția negativă a ecuației x*2-4=6 este ...​

Answer 1

Răspuns:

$x = -\sqrt{10}$

Explicație pas cu pas:

$x^2-4 = 6\Rightarrow x^2 - 10 = 0\\\Delta = 0 + 4\cdot 1 \cdot 10 = 40\Rightarrow \sqrt{\Delta} = \sqrt{40} = 2\sqrt{10}\\x_{1,2} = \frac{0\pm2\sqrt{10}}{2} = \pm \sqrt{10}\Rightarrow x_1 = -\sqrt{10}, x_2 = \sqrt{10}\Rightarrow x = x_1 = \boxed{-\sqrt{10}}$

Answer 2

 

$\displaystyle\\x^2-4=6\\\\x^2-4-6=0\\\\x^2-10=0\\\\(x-\sqrt{10} )(x+\sqrt{10} )=0\\\\x-\sqrt{10}=0\\\implies~\boxed{x_1=\sqrt{10}}\\\\x+\sqrt{10}=0\\\implies~\boxed{x_2=-\sqrt{10}}\\\\\text{Solutia negativa este: }~~\boxed{\bf~x_2=-\sqrt{10}}$