Question

Aplica +
7. Resolve a equação seguinte:
4(x2 + x) = 1 - x2​

Answer 1

Resposta:

S={ -1, 1/5 }

Explicação passo-a-passo:

4(x² + x) = 1 - x²

4​x²+4x=1-x²

4x²+x²+4x-1=0

5x²+4x-1=0

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~5x^{2}+4x-1=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=5{;}~b=4~e~c=-1\\\\C\'alculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(4)^{2}-4(5)(-1)=16-(-20)=36\\\\C\'alculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(4)-\sqrt{36}}{2(5)}=\frac{-4-6}{10}=\frac{-10}{10}=-1\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(4)+\sqrt{36}}{2(5)}=\frac{-4+6}{10}=\frac{2\div2}{10\div2}=\frac{1}{5}$

Answer 2

8+4x=1- 2x
8-1=2x-4x
7= -2x
X= 7: -2
X=-3,5