Question

Корень из x+17 - корень из x+1 =2

Answer 1

$\sqrt{x + 17} - \sqrt{x + 1} = 2 \\ \sqrt{ x+ 17} = 2 + \sqrt{x + 1} \\ x + 17 = 4 + 4 \sqrt{x + 1} + x + 1 \\ 17 = 4 + 4 \sqrt{x + 1} + 1 \\ 17 = 5 + 4 \sqrt{x + 1} \\ - 4 \sqrt{ x + 1} = 5 - 17 \\ - 4 \sqrt{x - 1} = - 12 \\ \sqrt{x + 1} = 3 \\ x + 1 = 9 \\ x = 9 - 1 \\ x = 8$