Question

Identify any extraneous soloution. See pic above

Answer 1

x = 3

Explanation:

Given

`√(-x+4)` = x - 4 ( square both sides )

- x 4 = (x - 4)² ← expand

- x + 4 = x² - 8x + 16 ( subtract - x + 4 from both sides )

0 = x² - 7x + 12 ← in standard form

0 = (x - 3)(x - 4) ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

As a check

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

x = 3 :
`√(-3+4)` =
`√(1)` = 1

right side = 3 - 4 = - 1

left side ≠ right side ⇒ extraneous solution

x = 4 :
`√(-4+4)` = 0 and right side = 4 - 4 = 0

left side = right side ⇒ x = 4 is the solution