Question

X²-10x-32=0, esta dando ∆=228, porem n tem raiz real, mas nao é negativo, oq devo fazer?

Answer 1

Resposta:

Fatore o número 228 para simplificar a expressão:

228 | 2

114 | 2

57 | 3

19 | 19

1 | 1  = 2 . 2 . 3 . 19 =2².3.19 =228

√228=√2².3.19=√2².√(3.19)=2√57

$\displaystyle\\Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-10x-32=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-10~e~c=-32\\\Delta=(b)^{2}-4(a)(c)=(-10)^{2}-4(1)(-32)=100-(-128)=228\\\sqrt{\Delta}=\sqrt{228}=2\sqrt{57}\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-10)-2\sqrt{57}}{2(1)}=\frac{10-2\sqrt{57}}{2}=5-\sqrt{57}\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-10)+2\sqrt{57}}{2(1)}=\frac{10+2\sqrt{57}}{2}=5+\sqrt{57}\\\\\\S=\{5-\sqrt{57}, 5+\sqrt{57}\}$