Question

Responda o Teorema de Pitagoras

Answer 1

(x + 9)² = (x + 3)² + (2x)²
x² + 2.9.x + 81 = x² + 2.3x + 9 + 4x²
x² + 18x + 81 = x² + 6x + 9 + 4x²
18x + 81 = 6x + 9 + 4x²
0 = 4x² - 18x + 6x + 9 - 81
0 = 4x² - 12x - 72 (:4)
0 = x² - 3x - 18 

x² - 3x - 18 = 0
a = 1; b = - 3; c = - 18

Δ = b² - 4ac
Δ = (-3)² - 4.1.(-18)
Δ = 9 + 72
Δ = 81

x = - b +/- √Δ = - ( - 3) +/- √81
           2a                2.1

x = 3 + 9 = 12/2 = 6
         2

x = 3 - 9 = - 6/2 = - 3  (descarta)
        2

2x =  2.6 = 12
x + 3 = 6 + 3 = 9
x + 9 = 6 + 9 = 15

R.:
x = 6
Hipotenusa (x + 9)= 15
cateto (x + 3) = 9
cateto (2x) = 12