Question

Determine no campo dos numeros inteiros o conjunto verdade das equações 2x ao Quadrado +1=3x

Answer 1

$2 x^{2} +1=3x\to\\2 x^{2} -3x+1=0\to\\ a=2;b=-3;c=1\\\\\Delta= b^{2} -4ac\to\Delta=(- 3)^{2} -4*2*1\to \Delta=9-8\to \Delta=1\\\\x= \frac{-b+- \sqrt{\Delta} }{2a} \to x= \frac{-(-3)+- \sqrt{1} }{2*2} \to x= \frac{3+-1 }{4} \to\\ \\ x'= \frac{3+1 }{4} \to x'= \frac{4 }{4} \to x'=1\\ \\ x''= \frac{3-1 }{4} \to x''= \frac{2 }{4} \to x''= \frac{1 }{2}\\\\ \\S=(1, \frac{1}{2} )$