Question

Calcule o valor das incógnitas a seguir:

Answer 1

Aplicando o Teorema de Pitágoras, temos:

a) x² = (5)² + (12)²

x² = 25 + 144

x² = 169

x = √169

x = 13

b) x² = (√10)² + (2√2)²

x² = 10 + 8

x² = 18

x = √18

x = 3√2

c) 6² = (x)² + (x)²

2x² = 36

x² = 36/2

x² = 18

x = √18

x = 3√2

d) (9 + x)² = (2x)² + (x + 3)²

9² + 18x + x² = 4x² + x² + 6x + 3²

81 + 18x + x² = 4x² + x² + 6x + 9

4x² + x² - x² + 6x - 18x + 9 - 81 = 0

4x² - 12x - 72 = 0    

Em que: a = 4,  b = - 12  e  c = - 72

x = - b ±√b² - 4ac / 2a

x = 12 ± √(-12)² - 4(4)(-72)  / 2(4)

x = 12 ± √144 + 1152  /  8

x = 12 ± √1296  / 8

x = 12 ± √36 / 8

x' = 12 + 6 / 8

x' = 18/8

x' = 9/4

x'' = 12 - 6 / 8

x'' = 6 / 8

x'' = 3/4

Bons estudos!