Question

Help please!!!

Answer 1

Answer:

x = $\frac{7+\sqrt{47}\times i }{4}$

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 = $(x-2)^{2}$         ---------------(2)

y = $(x-2)^{2}$ + 5         ---------------(3)

Substitute (3) in (1) ,

x + 2( $(x-2)^{2}$ + 5 ) = 6

$(a + b)^{2}$ =$a^{2} + 2ab + b^{2}$

x + 2( $x^{2} - 4x + 4$ + 5 ) = 6

$2x^{2} - 7x + 12=0$      --------------(4)

The roots of the quadratic equation $ax^{2} +bx+c$ is

x = $\frac{(-b) + \sqrt{(-b)^{2}-4 \times ac } }{2 \times a}$  -----------(5)

According to equation (5),solution of (4) is

x =  $\frac{7 + \sqrt{(-7)^{2}-4 \times 24 } }{2 \times 2}$

x =  $\frac{7+\sqrt{49-96}}{4}$

x = $\frac{7+\sqrt{47}\times i }{4}$