Question

Determine as raízes de equação por soma e produto a) x2 + 63 = 16x b) (x + 6)2 = 25x - 4

Answer 1

$a) \\ x^2+63=16x \\ \\ x^2-16x+63=0 \\ \\ (x-9)(x-7)=0 \\ \\ x-9=0~~~~~e~~~~x-7=0 \\ x=9~~~~~~~~~~~~~~~x=7 \\ \\ S=\{7,9\}$ 

$b) \\ (x+6)^2=25x-4 \\ \\ x^2+12x+36=25x-4 \\ \\ x^2+12x-25x+36+4=0 \\ \\ x^2-13x+40=0 \\ \\ (x-8)(x-5)=0 \\ \\ x-8=0~~~~~~~e~~~~~~~~x-5=0 \\ x=8~~~~~~~~~~~~~~~~~~~~~~x=5 \\ \\ ~S=\{5,8\}$