Question

encontre o conjunto solução das equações de 2° grau

a) x² - 8x + 15 = 0
b) 2x² - 162 = 0
c) 3x² - 5x = 0​

Answer 1

Resposta:

a).Solution set ={3,5}, b).  Solution set ={9,-9} c). Solution set ={0,5/3}  

Explicação p

asso a passo:

$(a)$

$x^{2} -8x+15=0\\\\x^{2} -5x-3x+15=0\\\\x(x-5)-3(x-5)=0\\\\(x-3)(x-5)=0\\\\x-3=0, x-5=0\\\\x=3, 5$

Solution set ={3,5}

$(b)$

$2x^{2} -162=0\\\\2(x^{2} -81)=0\\x^{2} -81=\frac{0}{2} \\\\ x^{2} -(9)^{2} =0\\\\(x+9)(x-9)=0\\\\x+9=0, x-9=0\\\\x=9, -9$  ∴  $x^{2} -y^{2} =(x+y)(x-y)$

Solution set ={9,-9}

$(c)\\\\3x^{2} -5x=0\\\\x(3x-5)=0\\\\x=0, 3x-5=0\\\\x=0, x=\frac{5}{3}$

Solution set ={0,5/3}