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!!!
