Question

calcule o valor de x nos triângulos retângulos​

Answer 1

Resposta:

a) x' = -1 e x'' = 3

b) x = 5

c) x' = -3 e x'' = 3

Explicação passo a passo:

h² = a² + b²

a) (x + 2)² = x² + (x + 1)²

x² + 4x + 4 = x² + x² + 2x + 1

x² + 4x + 4 = 2x² + 2x + 1

x² + 4x + 4 - 1 = 2x² + 2x

x² + 4x + 3 = 2x² + 2x

x² + 4x - 2x + 3 = 2x²

x² + 2x + 3 = 2x²

x² - 2x² + 2x + 3 = 0

-x² + 2x + 3 = 0

x = (-b ± √(b² - 4 • a • c)) / (2 • a)

x = (-2 ± √(2² - 4 • (-1) • 3)) / (2 • (-1))

x = (-2 ± √(4 - 4 • (-1) • 3)) / (-2)

x = (-2 ± √(4 + 12)) / (-2)

x = (-2 ± √16) / (-2)

x = (-2 ± √4²) / (-2)

x = (-2 ± 4) / (-2)

x = 1 ± (-2)

x' = 1 + (-2)

x' = 1 - 2

x' = - 1

x'' = 1 - (-2)

x'' = 1 + 2

x'' = 3

b) (x + 5)² = (x + 3)² + 6²

x² + 10x + 25 = x² + 6x + 9 + 36

x² + 10x + 25 = x² + 6x + 45

x² + 10x = x² + 6x + 45 - 25

x² + 10x = x² + 6x + 20

x² + 10x - 6x = x² + 20

x² + 4x = x² + 20

4x = 20

x = 20 / 4

x = 5

c) (2x)² = (3√3)² + x²

2²x² = 3²(√3)² + x²

4x² = 9 . 3 + x²

4x² = 27 + x²

4x² - x² = 27

3x² = 27

x² = 27 / 3

x² = 9

x = ±√9

x = ±√3²

x = ±3

x' = - 3

x'' = 3