Question

$\sqrt{x+7} + \sqrt{x-2} =9$

Answer 1

√ ( x + 7 ) + √ ( x - 2 ) = 9 
x ≥ - 7 ; x ≥ 2 
( √ ( x + 7 ) + √ ( x - 2 ))² = 9²
x + 7 + 2√(( x + 7 )( x - 2 )) + x - 2 = 81 
2√( ( x + 7 )( x - 2 )) = 81 - 2x - 5 
2√ ( ( x + 7 )( x - 2 )) = 2( 38 - x ) 
( √ ( x + 7 )( x - 2 ))² = ( 38 - x )²
( x + 7 )( x - 2 ) = 1444 - 76x + x²
x² - 2x + 7x - 14 = 1444 - 76x + x²
5x - 14 = 1444 - 76x 
76x + 5x = 1444 + 14 
81x = 1458 
x = 18 
Проверка 
√ ( 18 + 7 ) + √ ( 18 - 2 ) = 9 
√ 25 + √ 16 = 9 
5 + 4 = 9 
9 = 9 
ОТВЕТ 18

Answer 2

ОДЗ
{x+7≥0⇒x≥-7
{x-2≥0⇒x≥2
x∈[2;∞)
(√(x+7)+√(x-2))²=9²
x+7+2√(x²+5x-14)+x-2=81
2√(x²+5x-14)=76-2x
√(x²+5x-14=38-x
x²+5x-14=1444-76x+x²
5x+76x=1444+14
81x=1458
x=1458:81
x=18