hallo
|x| = 9 = √(x1²+x2²+x3²)
9 = √(x1²+x2²+x3²)
9 = √( ((28-32z)/81)² + ((-7+8z)/81)² + ((56-64z)/81)² )
9 = √( (28-32z)²/81² + (-7+8z)²/81² + (56-64z)²/81² )
9 = √( ((28-32z)² + (-7+8z)² + (56-64z)²)/81² )
9 = √( (28-32z)² + (-7+8z)² + (56-64z)²) ) / √(81²)
9 = √( (28-32z)² + (-7+8z)² + (56-64z)²) ) / 81
9*81 = √( (28-32z)² + (-7+8z)² + (56-64z)²) )
729² = (28-32z)² + (-7+8z)² + (56-64z)²)
729² = 1024*z² - 1792*z + 784 + 64*z² - 112*z + 49 + 4096*z² - 7168*z + 3136
729² = 5184*z² - 9072*z + 3969
5184*z²-9072*z-527472 = 0
pq oder mitternachtsformel benutzen, wir bekommen für z zwei lösungen:
z1 = 11, z2 = -37/4
probe z1 = 11
x1 = ((28-32*z1) : 81) = ((28-32*11)/81) = -4
x2 = ((-7+8*z1) : 81) = ((-7+8*11)/81) = 1
x3 = ((56-64*z1) : 81) = ((56-64*11)/81) = -8
x = (-4, 1, -8)
|x| = √((-4)²+1²+(-8)²) = √81 = 9 -> OK
probe z2 = -37/4
x1 = ((28-32*((-37)/4): 81) = -4
x2 = ((-7+8*((-37)/4)) : 81) = 1
x3 = ((56-64*((-37)/4)) : 81) = 8
x = (-4, 1, 8)
|x| = √((-4)²+1²+8²) = √81 = 9 -> OK
