Question

Agora resolva:
a) x2 - 3x + 2 = 0
b) y2 - 8y + 15 = 0
c) a2 - 16a + 63 = 0
d) y2 + 18y + 81 = 0

Answer 1

a) x² - 3x + 2 = 0

∆ = (-3)² - 4.1.2

∆ = 9 - 8

∆ = 1

$x = \frac{ - ( - 3) + - \sqrt{1} }{2 \times 1}$

$x = \frac{ 3 + - 1}{2}$

$x = \frac{3 + 1}{2} = 2$

$x = \frac{3 - 1}{2} = 1$

b) y² - 8y + 15 = 0

∆ = (-8²) - 4.1.15

∆ = 64 - 60

∆ = 4

$y = \frac{ - ( - 8) + - \sqrt{4} }{2 \times 1}$

$y = \frac{8 + - 2}{2}$

$y = \frac{8 + 2}{2} = 5$

$y = \frac{8 - 2}{2} = 3$

c) a² - 16a + 63 = 0

∆ = (-16)² - 4.1.63

∆ = 256 - 252

∆ = 4

$a = \frac{ - ( - 16) + - \sqrt{4} }{2 \times 1}$

$a = \frac{16 + - 2}{2}$

$a = \frac{16 + 2}{2} = 9$

$a = \frac{16 - 2}{2} = 7$

d) y² + 18y + 81 = 0

∆ = 18² - 4.1.81

∆ = 324 - 324

∆ = 0

$y = \frac{ - 18 + - \sqrt{0} }{2 \times 1}$

$y = \frac{ - 18 + - 0}{2}$

$y = \frac{ - 18}{2} = - 9$