Question

Решите уравнение √2х-6 - √х+1 = 2

Answer 1

V ( 2x - 6 ) - V ( X + 1 ) = 2
V ( 2x - 6 ) = 2 + V ( X + 1 )
( V ( 2x - 6))^2 = ( 2 + V ( X + 1 ))^2
2x - 6 = 4 + 4V( X + 1 ) + X + 1
2x - 6 - X - 1 - 4 = 4V( X + 1 )
X - 11 = 4V( X + 1 )
( X - 11)^2 = ( 4V( X + 1 ))^2
X^2 - 22x + 121 = 16( X + 1 )
X^2 - 22x + 121 = 16x + 16
X^2 - 38x + 105 = 0
D = 1444 - 420 = 1024 = 32^2
X1 = ( 38 + 32 ) : 2 = 35
X2 = ( 38 - 32 ) : 2 = 3
ОДЗ
1) 2х - 6 >=0 ; Х >= 0
2) Х + 1 >= 0 ; Х >= - 1
Ответ 3 ; 35