Question

Resolva a função quadrática

(3x-1)² + (x - 2)² = 25

Answer 1

$(3x-1)^2+(x-2)^2=25$


Expandindo os quadrados, temos

$(9x^2-6x+1)+(x^2-4x+4)=25\\\\ 9x^2+x^2-6x-4x+1+4=25\\\\ 10x^2-10x+5=25\\\\ 10x^2-10x+5-25=0\\\\ 10x^2-10x-20=0\\\\ 10\cdot (x^2-x-2)=0\\\\ x^2-x-2=0~~\Rightarrow~~\left\{\! \begin{array}{l} a=1\\b=-1\\c=-2 \end{array} \right.$

$\Delta=b^2-4ac\\\\ \Delta=(-1)^2-4\cdot 1\cdot (-2)\\\\ \Delta=1+8\\\\ \Delta=9\\\\\\ x=\dfrac{-b\pm \sqrt{\Delta}}{2a}\\\\\\ x=\dfrac{-(-1)\pm \sqrt{9}}{2\cdot 1}\\\\\\ x=\dfrac{1\pm 3}{2}\\\\\\ \begin{array}{rcl} x=\dfrac{1-3}{2}&~\text{ ou }~&x=\dfrac{1+3}{2}\\\\ x=\dfrac{-2}{2}&~\text{ ou }~&x=\dfrac{4}{2} \end{array}\\\\\\ ~~~\boxed{\begin{array}{rcl} x=-1&~\text{ ou }~&x=2 \end{array}}$


Conjunto solução: $S=\{-1,\,2\}.$