Question

O conjunto solução da equação 3/2(x+2)=1/2x-4-2/x^2-4 é?

Answer 1

$\frac{3}{2}(x+2)= \frac{\frac{1}{2x-4-2}}{x^2-4}$

$\frac{3}{2}(x+2)= \frac{x^2-4}{2x-4-2}$

$\frac{3x+2}{2}=\frac{x^2-4}{2x-4-2}$

$(3x+2).(2x-4-2)=2.(x^2-4)$

$6 x^{2} -12x-6x+4x-8-4=2 x^{2} -8$

$6 x^{2} -14x-12=2 x^{2} -8$

$4 x^{2} -14x-4=0$

$Δ= b^{2} -4.a.c \\ \\ x= \frac{-b+ou- \sqrt{Δ}}{2a}$

$Δ= (-14)^{2} -4.4.(-4) Δ= 196 +64=260$

$x= \frac{-(-14)+ou- \sqrt{260}}{2.4} \\ x= \frac{+14+ou- \sqrt{260} }{2.4} \\ x= \frac{14+ou-2 \sqrt{65} }{2.4} \\ x= \frac{7+ou-1 \sqrt{65} }{4}$

$x= \frac{7+\sqrt{65} }{4}$

$x= \frac{7-\sqrt{65} }{4}$

S={x∈R/$x= \frac{7+\sqrt{65} }{4}$ ou $x= \frac{7-\sqrt{65} }{4}$}