Question

como resolver e qual resultado dessa equação ?
x² + 2x - 31 = 0

Answer 1

Resposta:

S={-1-4√2, -1+4√2}

Explicação passo a passo:

$\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~x^{2}+2x-31=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=2~e~c=-31\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(2)^{2}-4(1)(-31)=4-(-124)=128$$\displaystyle C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(2)-\sqrt{128}}{2(1)}=\frac{-2-8\sqrt{2} }{2}=-1-4\sqrt{2}\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(2)+\sqrt{128}}{2(1)}=\frac{-2+8\sqrt{2} }{2}=-1+4\sqrt{2}\\\\S=\{-1-4\sqrt{2},~-1+4\sqrt{2}\}$

Obs.

√128

fatorando 128

128 | 2

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1 | 1

128 = 2 . 2 . 2 . 2 . 2 . 2 . 2 = 2⁶.2

√128=√2⁶.2=√2⁶.√2=2⁶/².√2=2³.√2=8√2