Question

Escreva o conjunto solução destas equações:
a)x²-10x=0
b)4m-m²=0
c)-3a²+6a=0
d)2y²+10y=0
e)3t+5t²=0
f)b²=-4b

Answer 1

a ) x² - 10x = 0
x² - 10x  0 = 0
a      b    c
Δ = b ² - 4 . a . c
Δ =( - 10 )² - 4 . 1 . 0 
Δ = 100 - 4 . 1 . 0
Δ = 100 - 0
Δ = 100

x = - b + ou - √Δ/ 2 . a
x = + 10 + ou - √100/ 2 . 1
x' = 10 + 10/ 2
x' = 20/ 2
x = 10

x'' = 10 - 10/ 2
x'' = 0/ 2
x'' = 0

S = { 10 , 0 }- RESPOSTA.

b ) 4m - m² = 0
- m² + 4m  0 = 0
   a       b    c
Δ = 4² - 4 . ( - 1 ) . 0
Δ = 16 + 0
Δ = 16

Daqui a diante eu simplificarei.

x' = - 4 + 4/ - 2
x' = 0/ - 2
x' = 0

x'' = - 4 - 4/ - 2
x' = - 8/ - 2
x' = 4

S = { 0, 4 }//

c ) - 3a² + 6 = 0
- 3a² 0 + 6 = 0
    a   b    c
Δ = 0² - 4 . ( - 3 ) . 6
Δ = 0 + 72
Δ = 72

x' = 0 + 72/ - 6
x' = 72/ - 6
x' = - 12

x'' = 0 - 72/ - 6
x'' = - 72/ - 6
x'' = 12

S = { - 12, 12 }

d ) 2y² + 10y = 0
2y² + 10y  0 = 0
 a        b    c
Δ = 10² - 4 . 2 . 0
Δ = 100 - 0
Δ = 0

x' = - 10 + 10/ 4
x' = 0/ 4
x' = 0

x'' = - 10 - 10/ 4
x'' = - 20/ 4
x'' = - 5

S = { 0, - 5 }

e ) 3t + 5t² = o
5t² + 3t  0 = 0
 a      b   c
Δ = 3² - 4 . 5 . 0
Δ = 9 - 0
Δ = 9

x' = - 3 + 3/ 10
x' = 0/ 10
x' = 0

x'' = - 3 - 3/ 10
x'' = - 9/ 10

S = { 0, - 9/ 10 }

f ) b² =  - 4b
b² + 4b 0 = 0
a       b  c
Δ = 4² - 4 . 1 . 0
Δ = 16 - 0
Δ = 16

x' = - 4 + 4/ 2
x' = 0/ 2
x' = 0

x'' = - 4 - 4/ 2
x'' = - 8/ 2
x'' = - 4

S = { 0, - 4 }

Bons estudos, Fabi.