Question

de o conjunto soluçao das seguintes equaçoes do 2 grau em e r: a) -49+
x elevado a 2=0 b) 36=4x elevado a 2 c)x elevado a 2 -5x=0 d)-7x+x elevado a 2=0 e) -4x elevado a 2 + 9x=0 f)3x elevado a 2 +5x=0 g) 4x elevado a 2 - 12x=0 h) x elevado a 2 =-x i) 7x elevado a 2 + 14x=0 j) -2x elevado a 2 + 10x =0 alguem por favor

Answer 1

a) -49 +x² =0
x² = 49
x= √49
x= +/- 7

S= { 7, -7 }

b) 36 = 4x²
-4x² = -36 . (-1)
4x² = 36
x²= 36/4
x²= 9
x= √9
x= +/- 3

S= { 3, -3 }

c) x² -5x = 0
x² -5x +0
Δ= b² -4ac
Δ= (-5)² -4.1.0
Δ= 25

x= -b +/- √Δ / 2a
x= -(-5) +/- √25 / 2.1
x'= 5 + 5 / 2
x'= 10/2
x'= 5

x''= 5 -5 / 2
x''= 0 / 2
x''= 0

S= { 5, 0 }

d) -7x +x² = 0
x² -7x +0
Δ= b² -4ac
Δ= (-7)² -4.1.0
Δ= 49

x= -b +/- √Δ / 2a
x= -(-7) +/- √49 / 2.1
x'= 7 + 7 / 2
x'= 14/ 2
x'= 7

x''= 7 -7 / 2
x''= 0/2
x''= 0

S= { 7,0 }

e) -4x²+ 9x = 0
-4x² +9x +0 . (-1)
4x² -9x +0
Δ= b² -4ac
Δ= (-9)² -4.4.0
Δ= 81

x= -b +/- √Δ / 2a
x= -(-9) +/- √81 / 2.4
x'= 9 + 9 / 8
x'= 18/ 8 (simplificando por 2)
x'= 6 /4 (simplificando por 2)
x'= 3/2

x''= 9 - 9 / 8
x''= 0/8
x''=0

S= { 3/2 , 0 }

f) 3x² +5x = 0
3x² +5x +0
Δ= b² -4ac
Δ= 5² -4.3.0
Δ= 25

x= -b +/- √Δ / 2a
x= -5 +/- √25 / 2.3
x'= -5 + 5 / 6
x'= 0 /6
x'= 0

x''= -5 -5 / 6
x''= -10 / 6 (simplificando por 2)
x''= -5/3

S= { 0, -5/3 }

g) 4x² -12x +0
Δ= b² -4ac
Δ=(-12)² -4.4.0
Δ= 144

x= -b +/- √Δ / 2a
x= -(-12) +/- √144 / 2.4
x'= 12 + 12 / 8
x'= 24/ 8
x'= 6

x''= 12 -12 / 8
x''= 0/8
x''= 0

S= { 6, 0 }

h) x² = -x
x² +x +0
Δ= b² -4ac
Δ= 1² -4.1.0
Δ= 1

x= -b +/- √Δ/ 2a
x= -1 +/- √1 / 2.1
x'= -1 +1 / 2
x''= 0/2
x'= 0

x''= -1 -1 / 2
x''= -2/2
x''= -1

S= { 0 , -1 }

i) 7x² +14x +0
Δ= b² -4ac
Δ= 14² -4.7.0
Δ= 196

x= -b +/- √Δ / 2a
x= -14 +/- √196 / 2.7
x'= -14 + 14 / 14
x'= 0 / 14
x'= 0

x''= -14 -14 / 14
x''= -28 / 14 (simplificando por 2
x''= -14/ 7 (simplificando por 7)
x''= -2/1
x''= -1

S= { 0, -1 }

j) -2x² +10x = 0
-2x² +10x +0 . (-2)
x² +5x +0
Δ= b² -4ac
Δ= 5² -4.1.0
Δ= 25

x= -b +/- √Δ / 2a
x= -5 +/- √25 / 2.1
x'= -5 + 5 / 2
x'= 0/2
x'= 0

x''= -5 -5 / 2
x''= -10 / 2
x''= -5

S= { 0, -5 }

Bons estudos!