√ ( 2x + 7 ) + √ ( 3x - 18 ) = √ ( 7x + 1 )
( √ ( 2x + 7 ) + √ ( 3x - 18 )) ² = ( √ 7x + 1 ) ²
2x + 7 + 3x - 18 + 2√( ( 2x + 7 )( 3x - 18 )) = 7x + 1
2√ ((2x + 7)( 3x - 18 )) = 7x + 1 - 5x + 11
2√(( 2x + 7 )( 3x - 18 )) = 2x + 12
√ (( 2x + 7 )( 3x - 18 )) = x + 6
( √ (( 2x + 7 )( 3x - 18 ))² = ( x + 6 )²
( 2x + 7 )( 3x - 18 ) = x² + 12x + 36
6x² - 36x + 21x - 126 = x² + 12x + 36
6x² - 15x - 126 = x² + 12x + 36
5x² - 27x - 162 = 0
D = 729 + 3240 = 3969 = 63²
X1 = ( 27 + 63 ) : 10 = 9
X2 = ( 27 - 63 ) : 10 = - 3,6
ОДЗ :
2x + 7 ≥ 0 ; x ≥ - 3,5
3x - 18 ≥ 0 ; x ≥ 6
7x + 1 ≥ 0 ; x ≥ - 1/7
ОТВЕТ ( - 3,6 ) ; 9