Question

a soma de dois números e 19 e o produto e 88. esses números são as raízes da equação.
a)x^+88x-19=0
b)x^-88x+19=0
c)x^+19x-88=0
d)x^-19x+88=0

Answer 1

$\left \{ {{x+y=19} \atop {x*y=88}} \right. \\\\\\ x+y=19\to x=-y+19\\\\\\ x*y=88\to (-y+19)*y=88\to -y^2+19y-88=0\\\\ a=-1;b=19;c=-88\\\\ \Delta=b^2-4ac\to \Delta=19^2-4*(-1)*(-88)\to \Delta=361-352\to \Delta= 9\\\\ y= \frac{-b\pm \sqrt{\Delta} }{2a} \to y= \frac{-19\pm \sqrt{9} }{2*(-1)} \to y= \frac{-19\pm 3 }{-2} \to \\\\ y'= \frac{-19+3 }{-2} \to y'= \frac{-16 }{-2} \to y'=8\\\\ y''= \frac{-19-3 }{-2} \to y''= \frac{-22 }{-2} \to y''=11$


$x'=-y+19\to x'=-8+19\to x'=11\\\\ x''=-y+19\to x''=-11+19\to x''=8\\\\\\ S= \left \{ (11;8);(8;11) \left \}$



$(x-x_{'})(x-x_{'})\to\\\\ (x-8)(x-11)\to\\\\ x^{2} -8x-11x+88\to \\\\ x^{2} -19x+88=0$



R.: Letra D) x²-19x+88=0