1) x² - 5x + 6 = 0
x = 5± 5² - 4.
6 2 x = 5± 25 - 24 2
x = 5± 1 2
x1 = 5 - 1 = 4 / 2 = 2 2
x2 = 5 + 1 = 6 / 2 = 3 2
2) 2x² - 7x + 3 = 0
x = 7² - 4.
2. 3 4
x = 49 - 24 4
x = 7± 25 4
x = 7±5 4
x1 = 12 / 4 = 3
x2 = 2 / 4 = 1 / 2
3) - x² + 7x - 10 = 0
( - 1) ( - x² + 7x - 10) = ( - 1).
0
x² - 7x + 10 = 0
x = 7± 7² - 4.
10 2
x = 7± 49 - 40 2
x = 7±9 2
x = 7±3 2
x1 = 10 / 2 = 5
x2 = 4 / 2 = 2
4) x² - 2x + 1 = 0
x = 2± 2² - 4.
1 2
x = 2± 4 - 4 2
x = 2± 0 2
x = 2±0 2
x = 2 / 2 = 1
x1 = 2 - 0 = 2 / 2 = 1 2
x2 = 2 + 0 = 2 / 2 = 1 2
lo mismo xD
5) x² - 4x + 4 = 0
x = 4± 16 - 16 2
x = 4 / 2
x = 2
6 ) 2x - 3 = 1 - 2x + x² x² - 4x + 4 = 0
x = 4± 16 - 16 2
x = 4 / 2 = 2
7) x² + (7 - x)² = 25 x² + 49 - 14x + x² = 25 x² - 7x + 12 = 0
x = 7± 49 - 48 2
x = 7±1 2
x1 = 7 + 1 / 2 = 4
x2 = 7 - 1 / 2 = 3
8) 7x² + 21x - 28 = 25 x² + 3x - 4 = 0
x = - 3 ± 9 + 16 2
x = - 3 ± 5 2
x1 = ( - 3) + 5 = 2 / 2 = 1 2
x2 = ( - 3) - 5 = - 8 / 2 = - 4 2
9) - x² + 4x - 7 = 0
x² - 4x + 7 = 0
x = 4 ± 16 - 28 2
x = - 3 ± - 12 2
Respuesta ; sale - raiz de 12 imaginario
10) 18 = 6x + x(x - 13)
18 = 6x + x² - 13x x² - 7x - 18 = 0 x = 7 ± 49 + 72 2 x = 7 ± 121 2
x = 7± 121 2
x1 = 18 / 2 = 9
x2 = - 4 / 2 = - 2.