Question

Radical Equations: How do I solve this?

Answer 1

(B). roots

Explanation:

(a ± b)² = a² ± 2ab + b²

~~~~~~~~

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

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

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

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

`√((4x+5)(x-1))` = 2x

(
`√((4x+5)(x-1))` )² = ( 2x )²

( 4x + 5 )( x - 1 ) = 4x²

4x² + x - 5 = 4x² ⇒ x = 5