Radical Equations: How do I solve this?

Question

asked Mar 18, 2023 176k views

1 Answer

Albert Ruelan · Answer 1 · 2023-03-24T14:27:38+0000

Answer:

(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