Question

The sum of the solutions of the equation `|sqrt(x) - 2|+ sqrt(x)(sqrt(x) - 4) + 2, (x > 0)` is equal to ______.

Options

• 12

• 9

• 10

• 4

Answer 1

The sum of the solutions of the equation `|sqrt(x) - 2|+ sqrt(x)(sqrt(x) - 4) + 2, (x > 0)` is equal to 10.

Explanation:

`|sqrt(x) - 2|+ sqrt(x)(sqrt(x) - 4) + 2` = 0

(i) For `sqrt(x) ≥ 2 ⇒ sqrt(x) - 2 + x - 4sqrt(x) + 2` = 0

`x - 3sqrt(x)` = 0

`sqrt(x)(sqrt(x) - 3)` = 0

x = 0|x = 9 ⇒ x = 9 is solution

(i) For `sqrt(x) < 2 ⇒ 2 - sqrt(x) + x - 4sqrt(x) + 2` = 0

`x - 5sqrt(x) + 4` = 0

`(sqrt(x - 4))(sqrt(x) - 1)` = 0 ⇒ x = 1|x = 16

⇒ x = 1 is solution

∴ Sum of solution = 1 + 9 = 10