Question

AJUDA PFV, UMA HORA ATE ACABAR!! Resolva as equações incompletas do 2º grau com 1 incógnita, em ℝ.

a) -5x² + 250 = 0

b) 3x² + 21x = 0

c) -2x² + x = 0

d) -5x² + 7x = 0

e) 6x² - 10x = 0

f) -2x² = 0

g) (x + 5)(x - 5) = 11

h) x²/10 - 3x/3 = 0

i) x - 6 = (x - 2)(x + 3)

j) x²-4/2 = x²-3

k) (3x + 1)² = 2(3x - 4)

l) x²/2 = x/5

Answer 1

a) $-5x^2+250=0$

$5x^2=250$

$x^2=\dfrac{250}{5}$

$x^2=50$

$x=\pm\sqrt{50}$

$x'=5\sqrt{2}$

$x"=-5\sqrt{2}$

b) $3x^2+21x=0$

$3x\cdot(x+7)=0$

$3x=0~\longrightarrow~x'=0$

$x+7=0~\longrightarrow~x=-7$

c) $-2x^2+x=0$

$x\cdot(-2x+1)=0$

$x'=0$

$-2x+1=0~\longrightarrow~2x=1~\longrightarrow~x"=\dfrac{1}{2}$

d) $-5x^2+7x=0$

$x\cdot(-5x+7)=0$

$x'=0$

$-5x+7=0~\longrightarrow~5x=7~\longrightarrow~x"=\dfrac{7}{5}$

e) $6x^2-10x=0$

$2x\cdot(3x-5)=0$

$2x=0~\longrightarrow~x'=0$

$3x-5=0~\longrightarrow~3x=5~\longrightarrow~x"=\dfrac{5}{3}$

f) $-2x^2=0$

$2x^2=0$

$x^2=0$

$x=\pm\sqrt{0}$

$x'=x"=0$

g) $(x+5)\cdot(x-5)=11$

$x^2-5^2=11$

$x^2-25=11$

$x^2=11+25$

$x^2=36$

$x=\pm\sqrt{36}$

$x'=6$

$x"=-6$

h) $\dfrac{x^2}{10}-\dfrac{3x}{3}=0$

$\dfrac{x^2}{10}-x=0$

$x^2-10x=0$

$x\cdot(x-10)=0$

$x'=0$

$x-10=0~\longrightarrow~x"=10$

i) $x-6=(x-2)\cdot(x+3)$

$x-6=x^2+x-6$

$x^2=0$

$x=\pm\sqrt{0}$

$x'=x"=0$

j) $\dfrac{x^2-4}{2}=x^2-3$

$x^2-4=2\cdot(x^2-3)$

$x^2-4=2x^2-6$

$2x^2-x^2=6-4$

$x^2=2$

$x=\pm\sqrt{2}$

$x=\sqrt{2}$

$x"=-\sqrt{2}$

k) $(3x+1)^2=2\cdot(3x-4)$

$9x^2+6x+1=6x-8$

$9x^2=-8-1$

$9x^2=-9$

$x^2=\dfrac{-9}{9}$

$x^2=-1$

Não há raízes reais

l) $\dfrac{x^2}{2}=\dfrac{x}{5}$

$5x^2=2x$

$5x^2-2x=0$

$x\cdot(5x-2)=0$

$x'=0$

$5x-2=0~\longrightarrow~5x=2~\longrightarrow~x=\dfrac{2}{5}$