Question

01) Resolva as equações incompletas abaixo:
a) x² – 4 = 0
b) 2x² – 32=0
c) 3x² – 24=0
d) 4x² – 20=0
e) 3x² +9=0
f) 9 + x2 = 0
g) x2 + 12 = 0
h) 2x² – 40=0
i) 42 - 7x2 = 0
1) 144 - 3x² = 0
k) 4x2 + 16 = 0
Rosolya
acões incomnl​

Answer 1

Explicação passo-a-passo:

$a) \: {x}^{2} - 4 = 0 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ x = 2$

$b) \: {2x}^{2} - 32 = 0 \\ {2x}^{2} = 32 \\ {x}^{2} = \frac{32}{2} \\ {x}^{2} = 16 \\ x = \sqrt{16} \\ x = 4$

$c) \: {3x}^{2} - 24 = 0 \\ {3x}^{2} = 24 \\ {x}^{2} = \frac{24}{3} \\ {x}^{2} = 8 \\ x = \sqrt{8} \\ x = 2 \sqrt{2}$

$d) \: {4x}^{2} - 20 = 0 \\ {4x}^{2} = 20 \\ {x}^{2} = \frac{20}{4} \\ {x}^{2} = 5 \\ x = \sqrt{5}$

$e) \: {3x}^{2} + 9 = 0 \\ {3x}^{2} = - 9 \\ {x}^{2} = - \frac{9}{3} \\ {x}^{2} = - 3$

$f) \: 9 + {x}^{2} = 0 \\ {x}^{2} = - 9$

$g) \: {x}^{2} + 12 = 0 \\ {x}^{2} = - 12$

$h) \: {2x}^{2} - 40 = 0 \\ {2x}^{2} = 40 \\ {x}^{2} = \frac{40}{2} \\ {x}^{2} = 20 \\ x = \sqrt{20} \\ x = 2 \sqrt{5}$

$i) \: 42 - {7x}^{2} = 0 \\ - {7x}^{2} = - 42 \\ - {x}^{2} = - \frac{42}{7} \\ { - x}^{2} = - 6 \: \: \: \times ( - 1) \\ {x}^{2} = 6 \\ x = \sqrt{6}$

$j) \: 144 - {3x}^{2} = 0 \\ - {3x}^{2} = - 144 \: \: \: \times ( - 1) \\ {3x}^{2} = 144 \\ {x}^{2} = \frac{144}{3} \\ {x}^{2} = 48 \\ x = \sqrt{48 } \\ x = 4 \sqrt{3}$

$k) \: {4x}^{2} + 16 = 0 \\ {4x}^{2} = - 16 \\ {x}^{2} = - \frac{16}{4} \\ {x}^{2} = - 4$