Question

Resolva a equação do 2grau sendo U=R
A)x²=1 B) x²=36 C)21=7x² D)2(x²-1)=x²+7 E) (x+1)(x-2)=3
F)3x²+5x=-x-9+2x² G)9x²-5=0

Answer 1

Olá!!

Resolução!!

a)

x² = 1
x = ± √1
x = ± 1
x' = + 1
x" = - 1

S = { - 1, + 1 }

b)

x² = 36
x = ± √36
x = ± 6
x' = + 6
x" = - 6

S = { - 6, + 6 }

c)

21 = 7x²
7x² = 21
x² = 21/7
x² = 3
x = ± √3
x' = + √3
x" = - √3

S = { - √3, + √3 }

d)

2 ( x² - 1 ) = x² + 7
2x² - 2 = x² + 7
2x² - 2 - x² - 7 = 0
2x²- x² - 7 - 2 = 0
x² - 9 = 0
x² = 9
x = ± √9
x = ± 3
x' = + 3
x" = - 3

S = { - 3, + 3 }

e)

( x + 1 ) ( x - 2 ) = 3
x² - 2x + 1x - 2 = 3
x² - x - 2 - 3 = 0
x² - x - 5 = 0

a = 1, b = - 1, c = - 5

∆ = b² - 4ac
∆ = ( - 1 )² - 4 • 1 • ( - 5 )
∆ = 1 + 20
∆ = 21

x = - b ± √∆ / 2a
x = - ( - 1 ) ± √21/2 • 1
x = 1 ± √21/2
x' = 1 + √21/2
x" = 1 - √21/2

S = { 1 - √21/2, 1 + √21/2 }

f)

3x² + 5x = - x - 9 + 2x²
3x² + 5x + x + 9 - 2x² = 0
3x² - 2x² + 5x + x + 9 = 0
x² + 6x + 9 = 0

a = 1, b = 6, c = 9

∆ = b² - 4ac
∆ = 6² - 4 • 1 • 9
∆ = 36 - 36
∆ = 0

x = - b ± √∆ / 2a
x = - 6 ± √0 / 2 • 1
x = - 6 ± 0 / 2
x' = x" = - 6/2
x' = x" = - 3

S = { - 3 }

g)

9x² - 5 = 0
9x² = 5
x² = 5/9
x = ± √5/9
x = ± √5/√9
x = ± √5/3
x' = + √5/3
x" = - √5/3

S = { - √5/3, + √5/3 }

Espero ter ajudado!!