Answer:
x = [tex]\frac{7+\sqrt{47}\times i }{4}[/tex]
Step-by-step explanation:
To solve quadratic systems,we always substitute one variable in terms if the other and then solve the equation.
x + 2y = 6 ---------------(1)
y - 5 = [tex](x-2)^{2}[/tex] ---------------(2)
y = [tex](x-2)^{2}[/tex] + 5 ---------------(3)
Substitute (3) in (1) ,
x + 2( [tex](x-2)^{2}[/tex] + 5 ) = 6
[tex](a + b)^{2}[/tex] =[tex]a^{2} + 2ab + b^{2}[/tex]
x + 2( [tex]x^{2} - 4x + 4[/tex] + 5 ) = 6
[tex]2x^{2} - 7x + 12=0[/tex] --------------(4)
The roots of the quadratic equation [tex]ax^{2} +bx+c[/tex] is
x = [tex]\frac{(-b) + \sqrt{(-b)^{2}-4 \times ac } }{2 \times a}[/tex] -----------(5)
According to equation (5),solution of (4) is
x = [tex]\frac{7 + \sqrt{(-7)^{2}-4 \times 24 } }{2 \times 2}[/tex]
x = [tex]\frac{7+\sqrt{49-96}}{4}[/tex]
x = [tex]\frac{7+\sqrt{47}\times i }{4}[/tex]
