Question

Sendo t ≠ 3, determine os valores reais de t para que se tenha t – 5 = 1/(t - 3) (faça o cálculo)​

Answer 1

$\sf{t-5=\dfrac{1}{t-3}}\\\sf{(t-5)\cdot(t-3)=1}\\\sf{t^2-8t+15=1}\\\sf{t^2-8t+15-1=0}\\\sf{t^2-8t+14=0}\\\sf{\Delta=(-8)^2-4\cdot1\cdot14}\\\sf{\Delta=64-56}\\\sf{\Delta=8}\\\sf{t=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\sf{t=\dfrac{-(-8)\pm\sqrt{8}}{2\cdot1}}\\\sf{t=\dfrac{8\pm2\sqrt{2}}{2}}\\\sf{t=\dfrac{\diagup\!\!\!\!2\cdot(4\pm\sqrt{2})}{\diagup\!\!\!\!2}}\\\sf{t=4\pm\sqrt{2}}\begin{cases}\sf{t_1=4+\sqrt{2}}\\\sf{t_2=4-\sqrt{2}}\end{cases}$