Question

resolver estás ecuaciones cuadráticas con el método de complementar el cuadro:
ײ—9×+14=0
4ײ—4×+1=0
ײ—6×+3=0
ME PUEDEN AYUDARR PORFIIIS ​

Answer 1

Respuesta:

x² - 9x + 14 = 0

x² - 9x = -14

x² - 2•9x/2 = -14

x² - 2•9x/2 + (9/2)² = -14 + (9/2)²

(x - 9/2)² = -56/4 + 81/4

(x - 9/2)² = 25/4

√(x - 9/2)² = √(25/4)

| x - 9/2 | = 5/2

x - 9/2 = ±5/2

x = - 9/2 ± 5/2

x1 = 5/2 - 9/2 = -4/2 = -2

x2 = -9 - 5/2 = -14/2 = -7

4x² - 4x + 1 = 0

(2x)² - 2•1•2x + 1² = 0

(2x - 1)² = 0

[2(x - ½)]² = 0

2²(x - ½)² = 0

4(x - ½)² = 0

Ambas soluciones son la misma: 1/2

x² - 6x + 3 = 0

x² - 2•3•x + 3 = 0

x² - 2•3•x + 3 + 6 = 6

x² - 2•3•x + 9 = 6

x² - 2•3•x + 3² = 6

(x - 3)² = 6

√(x - 3)² = √6

| x - 3 | = √6

x - 3 = ±√6

x = 3 ± √6

x1 = 3 + √6

x2 = 3 - √6

Saludos! :)