√(x+17) - √(x+1) =2
ОДЗ: x+17≥0 x+1≥0
x≥ -17 x≥ -1
x∈[-1; +∞)
(√(x+17) - √(x+1))² = 2²
x+17 - 2√[(x+17)(x+1)]+x+1 =4
2x+18 - 2√(x²+17x+x+17) =4
-2√(x²+18x+17)= -2x+4-18
-2√(x²+18x+17)= -2x -14
√(x²+18x+17) = x+7
x²+18x+17=(x+7)²
x²+18x+17=x²+14x+49
x²-x²+18x-14x=49-17
4x=32
x= 8
Ответ: 8