Question

Resolva os sistemas de duas equações do 2º grau.

A) X+Y = 5/6
X²+3Y = 5/4

B) X+Y= 5
X-Y²= 3

Ajuda por favor

Answer 1

A)

x+y=5/6
x^2+3y=5/4

x=-y+5/6
(-y+5/6)^2+3y=5/4
(-y+5/6),(-y+5/6) +3y=5/4

y^2-5/6y-5/6y+25/36=5/4

y^2-10/6y+25/36-5/4=0

y^2-10/6y-5/9=0

y^2-5/3y-5/9=0

delta=b^2-4.a.c
delta=(-5/3)^2-4.1.-5/9
delta=25/9+20/9
delta=45/9
delta=5

x'=
$-b + ou - \sqrt{delta} \div 2 \times \: a$
$- ( - \frac{5}{3} ) + \sqrt{5} \div 2 \\ \frac{5}{3} \div 2 \\ \frac{5}{3} \times \frac{1}{2} = \frac{5}{6}$

$\frac{5}{6} + \sqrt{5} \div 2$
$5 + 3 \sqrt{5} \div 6$
x"=
$\frac{5}{3} - \sqrt{5} \div 2 \\ 5 - 3 \sqrt{5} \div 6$