Question

Answer and tell me how you got answer thanks.

Answer 1

B

Explanation:

Given

`√(x+2)` = - x ( square both sides )

x + 2 = (- x)² = x² ( subtract x + 2 from both sides )

0 = x² - x - 2 ← in standard form

0 = (x - 2)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x + 1 = 0 ⇒ x = - 1

As a check

Substitute these values into the equation and if both sides are equal then it is a solution.

x = 2 : left =
`√(2+2)` =
`√(4)` = 2, right side = - 2 ← not equal

Thus x = 2 is an extraneous solution

x = - 1 : left =
`√(-1+2)` =
`√(1)` = 1 , right side = - (- 1) = 1 ← equal

Thus the solution is { - 1 } → B

Answer 2

A) {-1,2}

Explanation:

square both side of the equation. Then:

x+2=x^2

simplify:

x^2-x-2=0

factor:

(x+1)(x-2)=0

then:

x=-1, x=2