Question

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 1

D) -1.8

`-1.8`

Answer 2

x = -1.8 two equations approximately equal.

Explanation:

Given : y =
`(1)/((x+2))` ,y =
`y = x^(2) +2`

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

Solution : We have given that

y =
`(1)/((x+2))` -----( equation 1)

`y = x^(2) +2`------( equation 2).

Plug the of equation 2 in 1

`x^(2) +2` =
`(1)/((x+2))`.

`x^(2)(x+2) +2(x+2)` = 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.