Question

How do I solve this equation and check all the solutions?

Answer 1

x = 12

Explanation:

`√(3x)` + 10 = x + 4

`√(3x)` = x - 6

(
`√(3x)` )² = ( x - 6 )²

3x = x² - 12x + 36

x² - 15x + 36 = 0

(x - 3)(x - 12) = 0

`x_(1)` = 3

`x_(2)` = 12

Check the answer:

`√(3*3)` + 10 ≠ 3 + 4

13 ≠ 7 ⇒ 3 is not the root of original equation (strange root)

`√(3*12)` + 10 = 12 + 4

16 = 16 ⇒ 12 is the root of original equation