Which of the following is an extraneous solution of StartRoot 4 x + 41 EndRoot = x + 5?

x = - 8 is an extraneous solution

Step-by-step explanation:

Given

= x + 5 ( to clear the radical, square both sides )

4x + 41 = (x + 5)² ← expand using FOIL

4x + 41 = x² + 10x + 25 ( subtract 4x + 41 from both sides )

0 = x² + 6x - 16 ← in standard form

0 = (x + 8)(x - 2) ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 2 = 0 ⇒ x = 2

As a check

Substitute these values into the equation and if both sides are equal then they are solutions.

x = - 8

left side = = = 3

right side = - 8 + 5 = - 3 ≠ 3 → Thus not a solution

x = 2

left side = = = 7

right side = 2 + 5 = 7 → thus a solution

x = 2 is a solution and x = - 8 is an extraneous solution

15 units use socratic

step-by-step explanation: 15 units