Question

1-)resolva as equações do 2º grau incompletas abaixo :
a)x² - 49 =0
b)x²=1
c)2x² - 50 =0
d)7x² - 7=0
e)5x² +15 =0
f)21=7x²

Answer 1

a)
$x^{2} -49=0$

$x^{2} =49$

$x^{2} = \sqrt{49}$

x'=7
x"=-7

S={-7,7}

b)
$x^{2} =1$

$x^{} = \sqrt{1}$

x'=1
x"=-1

S={-1,+1}

c)
$2 x^{2} -50=0$

$2 x^{2} =50$

$x^{2} = \frac{50}{2}$

$x^{2} =25$

$x^{} = \sqrt{25}$
x'=5
x"=-5

S={-5,5}

d)
$7 x^{2} -7=0$

$7 x^{2} =7$

$x^{2} = \frac{7}{7}$

$x^{2} =1$

$x^{} = \sqrt{1}$

x'=1
x"=-1

S={-1,1}

e)
$5 x^{2} +15=0$

$5 x^{2} =-15$

$x^{2} = \frac{-15}{3}$

$x^{2} =-3$

$x^{} = \sqrt{-3}$∉R

S={  }

f)
$21=7 x^{2}$

$7 x^{2} =21$

$x^{2} = \frac{21}{7}$

$x^{2} =3$

$x^{} = \sqrt{3}$

$x^{'} = \sqrt{3}$

$x^{"} =- \sqrt{3}$

S={$\sqrt{3} , -\sqrt{3}$}

g)
$5 x^{2} +20=0$

$5 x^{2} =-20$

$x^{2} = \frac{-20}{5}$

$x^{2} =-4$

$x^{} = \sqrt{-4}$∉R

S={  }

h)
$7 x^{2} +2=30$

$7 x^{2} =30-2=28$

$x^{2} = \frac{28}{7}$

$x^{2} =4$

$x^{} = \sqrt{4}$

x'=2
x"=-2

S={-2,2}