The solution to this system of equations lies between the x-values -2 and -1.5. At which x-value are the two equations approximately equal?

y=1/(x+2)
y=x^2+2

A) -1.5
B) -1.6
C) -1.7
D) -1.8

Answer:

x = -1.8  two equations approximately equal.

Step-by-step explanation:

Given : y = [tex]\frac{1}{(x+2)}[/tex] ,y =[tex]y = x^{2} +2[/tex]

To find : which x-value are the two equations approximately equal.

Solution  : We have given that

y = [tex]\frac{1}{(x+2)}[/tex] -----( equation 1)

[tex]y = x^{2} +2[/tex]------( equation 2).

Plug the of equation 2 in 1

[tex]x^{2} +2[/tex] =  [tex]\frac{1}{(x+2)}[/tex].

[tex]x^{2}(x+2) +2(x+2)[/tex] = 1.

x³+2x² +2x+4 = 1

On subtracting 1 both sides.

x³+2x² +2x+3 = 0

For x = -1.8

Therefore,  x = -1.8  two equations approximately equal.