Question

GENTEE, PLDD, TO DESESPERADA, SCRR, É PARA AMANHÃ ISSO, TO PEDINDO AJUDA NA MORALZINHA​

Answer 1

a)

${5x}^{2} = 0 \\ x = 0$

.

S = 0

b)

${x}^{2} - 7x = 0 \\ x(x - 7) = 0 \\ x = 0 \: ou \: x = 7$

.

S = {0;7}

c)

${3x}^{2} - 6x = 0 \\ 3x(x - 2) = 0 \\ x = 0 \: ou \: x = 2$

S = {0;2}

d)

${x}^{2} - 7 = 0 \\ x = ± \sqrt{7}$

S = {-√2;√2}

e)

${x}^{2} + 25 = 0 \\ {x}^{2} = - 25$

S = Ø

f)

$- {3x}^{2} + 7 = 0 \\ - {3x}^{2} = - 7 \\ {x}^{2} = \frac{7}{3} \\ x =± \sqrt{ \frac{7}{3} }$

S = {-√7/3; √7/3}

g)

${x}^{2} - 7x + 6 = 0 \\ Δ = 25$

$x = \frac{7± \sqrt{25} }{2} \\ x1 = \frac{7 + 5}{2} = 6 \\ x2 = \frac{7 - 5}{2} = 1$

S = {1;6}

h)

${x}^{2} + 10x + 25 = 0 \\ {(x + 5)}^{2} = 0 \\ x = - 5$

S = {-5}

4)a)

${(x + 3)}^{2} = 1 \\ {x}^{2} + 6x + 8 = 0 \\ Δ = 4 \\ x = \frac{ - 6± \sqrt{4} }{2} \\ x1 = \frac{ - 6 + 2}{2} = - 2 \\ x2 = \frac{ - 6 - 2}{2} = - 4$

S = {-4;-2}

b)

${(2x - 4)}^{2} = 0 \\ 2x - 4 = 0 \\ 2x = 4 \\ x = 2$

S = {2}

c)

${( x - 3)}^{2} = {2x}^{2} \\ {x}^{2} + 6x - 9 = 0 \\ Δ = 72 \\ x = \frac{ -6± \sqrt{72} }{2} \\ x1 = \frac{ - 6 + 6 \sqrt{2} }{2} = -3 + 3 \sqrt{2} \\ x2 = \frac{ - 6 - 6 \sqrt{2} }{2} = - 3 - 3 \sqrt{2}$

d)

$x.(3x + 4) = - 1 \\ {3x}^{2} + 4x + 1 = 0 \\ Δ = 4 \\ x = \frac{ -4 ± \sqrt{4} }{6} \\ x1 = \frac{ - 4 + 2}{6} = \frac{ - 2}{6} = \frac{ - 1}{3} \\ x2 = \frac{ - 4 - 2}{6} = - 1$

S = {-1/3;-1}

e)

$\frac{ {x}^{2} }{2} + x = 0 \\ {x}^{2} + 2x = 0 \\ x(x + 2) = 0 \\ x = 0 \: ou \: x = - 2$

S = {0;-2}

f)

$(x - 3).(x + 3) = 0 \\ x - 3 = 0 \: ou \: x + 3 = 0 \\ x = 3 \: ou \: x = - 3$

S = {-3;3}

g)

$\frac{ {5x}^{2} }{3} - \frac{2x}{5} = 0 \\ \frac{ {25x}^{2} - 6x}{15} = 0 \\ {25x}^{2} - 6x = 0 \\ x(25x - 6) = 0 \\ x = 0 \: ou \: x = \frac{6}{25}$

S = {0;6/25}