Respuesta :
Answer:
Exact Form:
t = 2 ± 2√2
Decimal Form:
t = 4.82842712, − 0.82842712
Step-by-step explanation:
[tex]\bf 3(t^2-1)=2t^2+4t+1\implies 3t^2-3=2t^2+4t+1\implies t^2-3=4t+1 \\\\\\ t^2-4t-3=1\implies t^2-4t-4=0 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}t^2\stackrel{\stackrel{b}{\downarrow }}{-4}t\stackrel{\stackrel{c}{\downarrow }}{-4} \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t=\cfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(-4)}}{2(1)}\implies t=\cfrac{4\pm\sqrt{16+16}}{2}[/tex]
[tex]\bf t=\cfrac{4\pm\sqrt{4^2+4^2}}{2}\implies t=\cfrac{4\pm\sqrt{2(4^2)}}{2}\implies t=\cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\pm \stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\sqrt{2}}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \\\\\\ t = 2\pm 2\sqrt{2}\implies t\approx \begin{cases} 4.828427124746191\\ -0.8284271247461907 \end{cases}[/tex]
