Question

a) 5 = x² - 4x + 9
c) 45(x²+ 1) = 60
b) (3x + 1)² = 6x + 1
d) (3m + 5)² = 5(m+5)​

Answer 1

Resposta:

a) x = 2

b) x¹ = - √3/3 x² = √3/3

c) x = 0

d) m¹ = -25/9 m² = 0

Explicação:

a) 5 = x² - 4x + 9

5 - x² + 4x - 9 = 0

- 4 - x² +4x = 0

4 + x² - 4x = 0

x² - 4x + 4 = 0

(x -2)² = 0

x - 2 = 0

x = 2

b) 45 (x²+1) = 60

3 (x² + 1) = 4

3x² + 3 = 4

3x² = 4 - 3

3x² = 1

x² = 1/3

x = +- √3/3

x¹ = - √3/3 x² = √3/3

c) (3x +1)² = 6x +1

9x² + 6x +1 = 6x +1

9x² = 0

x² = 0

x = 0

d) (3m + 5)² = 5 (m + 5)

9m² + 30m + 25 = 5m + 25

9m² +30m = 5m

9m² +30m - 5m = 0

9m² + 25m = 0

m • (9m + 25) = 0

m = 0

9m + 25 = 0 m

m = 0

m = -25m/9

m¹ = -25/9 m² = 0