Question

14- Calcular as equações:
a) x² + 9x + 8 = 0
b) 9x2 - 24x + 16 = 0
c) x² - 2x+4=0
d) 10x² + 72x - 64 = 0
e) x²-3x - 4 = 0
f) 5x²-3x - 2=0
g)x² -10x+25=0
h) 3x2 - 15x + 12 = 0
i) x²-x- 20=0
j) x² - 8x + 7 = 0
Urgente,alguém me ajuda por favor,vou até dar 15 pontos​

Answer 1

Resposta:

a) -1 e -8

b) 1,33

c) X∉R

d) -1,039 e -6,161

e) 4 e -1

f) -0,4 ou -2/5

g) 5

h) 4 e 1

i) 5 e - 4

j) 7 e 1

Explicação passo a passo:

a) x² + 9x + 8 = 0

Δ=$9^{2}$-4*1*8 ----> Δ=81-32 ---> Δ=49

X=$\frac{-9 +\sqrt{49} }{2}$ ---> X= -1

X=$\frac{-9 -\sqrt{49} }{2}$ ---> X = -8

b) 9x2 - 24x + 16 = 0

Δ=$24^{2}$-4*9*16 ----> Δ=576-576 ---> Δ=0

X=$\frac{24 }{18}$ ---> X= 1,33

c) x² - 2x+4=0

Δ=$2^{2}$-4*1*4 ----> Δ=4-16 ---> Δ=-12

X=$\frac{-2 +\sqrt{-12} }{2}$ ---> $\sqrt{-12}$∉R, logo X∉R

d)10x² + 72x - 64 = 0

Δ=$72^{2}$-4*10*(-64) ----> Δ=5184-2560 ---> Δ=2624

X=$\frac{-72 +\sqrt{2624} }{20}$ ---> X= -1,039

X=$\frac{-72 -\sqrt{2624} }{20}$ --->X = -6,161

e) x²-3x - 4 = 0

Δ=$3^{2}$-4*1*(-4) ----> Δ=9+16 ---> Δ=25

X=$\frac{3 +\sqrt{25} }{2}$ ---> X= 4

X=$\frac{3 -\sqrt{25} }{2}$ ---> X = -1

f) 5x²-3x - 2=0

Δ=$3^{2}$-4*5*(-2) ----> Δ=9+40 ---> Δ=49

X=$\frac{3 +\sqrt{49} }{10}$ ---> X= 1

X=$\frac{3 -\sqrt{49} }{10}$ ---> X = -0,4 ou -2/5

g) x² -10x+25=0

Δ=$10^{2}$-4*1*25 ----> Δ=100-100 ---> Δ=0

X=$\frac{10 +-\sqrt{0} }{2}$ ---> X= 5

h) 3x2 - 15x + 12 = 0

Δ=$15^{2}$-4*3*12 ----> Δ=225-144 ---> Δ=81

X=$\frac{15 +\sqrt{81} }{6}$ ---> X= 4

X=$\frac{15 -\sqrt{81} }{6}$ ---> X = 1

i) x²-x- 20=0

Δ=$1^{2}$-4*1*(-20) ----> Δ=1+80 ---> Δ=81

X=$\frac{1 +\sqrt{81} }{2}$ ---> X= 5

X=$\frac{1 -\sqrt{81} }{2}$ ---> X = - 4

j) x² - 8x + 7 = 0

Δ=$8^{2}$-4*1*7 ----> Δ=64-28 ---> Δ=36

X=$\frac{8+\sqrt{36} }{2}$ ---> X= 7

X=$\frac{8-\sqrt{36} }{2}$ ---> X = 1