Question

Which statement about sqrt x- sqrt (x-5) =1 is true? x = 4 is a true solution. x = 4 is an extraneous solution. x = 9 is a true solution. x = 9 is an extraneous solution.

Answer 1

Answer:

x = 9 is a true solution

Step-by-step explanation:

Given:

√x - √(x - 5) = 1

This is irrational equation with next conditions:

x ≥ 0 and x - 5 ≥ 0  => x ≥ 0 and x ≥ 5 => x ≥ 5

√x - √(x - 5) = 1 => √x = 1 + √(x - 5)

now we will square both sides of equation and get:

x = x - 5 + 2 √(x - 5) + 1  => 2 √(x - 5 = x - x + 5 - 1 => 2 √(x - 5) = 4

now we will divide both sides with 2 and get:

√(x - 5) = 2

now we will square both sides of equation and get:

x - 5 = 4 => x = 4 + 5 = 9   => x = 9

since that this solution satisfies the given condition x ≥ 5 is accepted as final

x = 9

Check:

√9 - √(9 - 5) = 1  => 3 - √4 = 1  => 3 - 2 = 1  => 1 = 1   It's true

God with you!!!