Question

determine em   R   , o conjunto soluçao das seguintes equaçoes do 2 grau:

 

 

A)  x² - 9x=o --------->

 

 

B) 16y² =9------------->

 

 

c)x²-49=0-------------->

 

 

 

D)m² +m=o---------------->

 

 

 

e)3x² -60=0------------------>

 

 

 

f)6y²  -2y=0---------------->

 

 

 

Answer 1

Primeiramente faça isso x²-9x=0 é a mesma coisa que x(x-9)=0

agora você vai achar a raiz da função que é x-9=0 -> x=9

vamos verificar

9²-9.9=0

81-81=0

 

16y²=9 -> $<var>y^{2}=\frac{9}{16}\\ y=\sqrt\frac{9}{16}\\y=\sqrt\frac{3^{2}}{4^{2}}\\y=\frac{3}{4}</var>$

 

vamos testar 16$<var>16.\frac{3^{2}}{4^{2}}=9\\\\\frac{16.9}{16}=9</var>$

 

c)x²-49=0 então x²=49 ->$<var>x=\sqrt49\\\\x=7</var>$

vamos testar 7²-49=0

49-49=0

 

d)m²-m=0 (-1)²+(-1)=0; 1-1=0

 

e)3x²-60=0 -> 3x²=60 -> x²=20 -> x=raiz de 20

 

f)6y²-2y=0 -> (isole o y) y(6y-2)=0 ach a raiz 6y-2=0, 6y=2, y=2/6, y=1/3.

vamos testar 

$<var>6y^{2}-2y=0\\\\\frac{6.1^{2}}{3^{2}}-\frac{2.1}{3}=0\\\\\frac{6}{9}-\frac{2}{3}=0\\\\simplificando\ 6\ e\ 9\ por\ 3\ temos\ \frac{2}{3}\\logo\ \frac{2}{3}-\frac{2}{3}=0</var>$

Answer 2

a) $\text{x}^2-9\text{x}=0$

 

$\text{x}\cdot(\text{x}-9)=0$

 

$\text{x}'=0$

 

$\text{x}"=9$

 

 

b) $16\text{y}^2=9$

 

$\text{y}^2=\dfrac{9}{16}$

 

$\text{y}=\pm\sqrt{\dfrac{9}{16}}=\pm\dfrac{3}{4}$

 

 

c) $\text{x}^2-49=0$

 

$\text{x}^2=49$

 

$\text{x}=\pm\sqrt{49}=\pm7$

 

 

 

d) $\text{m}^2+\text{m}=0$

 

$\text{m}\cdot(\text{m}+1)=0$

 

$\text{m}'=0$

 

$\text{m}"=-1$

 

 

e) $3\text{x}^2-60=0$

 

$3\text{x}^2=60$

 

$\text{x}^2=20$

 

$\text{x}=\pm\sqrt{20}=\pm2\sqrt{5}$

 

 

 

f) $6\text{y}^2-2\text{y}=0$

 

$2\text{y}\cdot(3\text{y}-1)=0$

 

$\text{y}'=0$

 

$\text{y}"=\dfrac{1}{3}$