Question

Ayudenme a resolver las siguientes ecuaciones :(
X2+2x+32=0

X2+8x+16=48+16

9x2+18x+17=0

Answer 1

X² + 2X + 32 = 0 (Ecuacion de segundo grado)

Donde: a = 1; b = 2; c = 32

$X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X=\frac{-2\pm \sqrt{(2)^2-4(1)(32)}}{2(1)}$

$X=\frac{-2\pm \sqrt{4-128}}{2}$

$X=\frac{-2\pm \sqrt{-124}}{2}$

$X=\frac{-2\pm \sqrt{-(4)(31)}}{2}$

$X=\frac{-2\pm 2\sqrt{31} i}{2}$

X = - 1 +/- 2√(31) i

X1 = -1 + 2√(31) i

X2 = -1 - 2√(31) i

X² + 8X + 16 = 48 + 16

X² + 8X + 16 - 48 - 16 = 0

X² + 8X - 48 = 0

Donde: a = 1; b = 8; c = -48

$X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X=\frac{-8\pm \sqrt{(8)^2-4(1)(-48)}}{2(1)}$

$X=\frac{-8\pm \sqrt{64+192}}{2}$

$X=\frac{-8\pm \sqrt{256}}{2}$

$X=\frac{-8\pm \ 16}{2}$

X1 = (-8 + 16)/2 = 8/2 = 4

X1 = 4

X2 = (-8 - 16)/ = -24/2 = -12

X2 = -12

X1 = 4;  X2 = -12

9X² + 18X + 17 = 0

a = 9; b = 18; c = 17

$X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X=\frac{-18\pm \sqrt{(18)^2-4(9)(17)}}{2(9)}$

$X=\frac{-18\pm \sqrt{324-621}}{18}$

$X=\frac{-18\pm \sqrt{-288}}{18}$

$X=\frac{-18\pm \sqrt{-(144)(2)}}{18}$


$X=\frac{-18\pm 12\sqrt{(2)}i}{18}$

$X = -1\pm\frac{2\sqrt{2}}{3}i$

$X1 = -1+\frac{2\sqrt{2}}{3}i$

$X2 = -1 - \frac{2\sqrt{2}}{3}i$