Question

Розвяжіть рівняння
1)√х+4=х+2
2)√х+5+1=х

Answer 1

1)

$\sqrt{x} = x + 2 - 4 \\ \sqrt{x} = x - 2 \\ x = x {}^{2} - 4x + 4 \\ x - x {}^{2} + 4x - 4 = 0 \\ x \times (1 - x) + 4x - 4 = 0 \\ x \times (1 - x) - 4( - x + 1) = 0 \\ (1 - x) \times (x - 4) = 0 \\ x = 1 \\ x = 4 \\ \sqrt{1} + 4 = 1 + 2 \\ \sqrt{4} + 4 = 4 + 2 \\ 5 = 3 \\ 6 = 6 \\ x = 4</p><p>$

2)

$\sqrt{x} + 6 = x \\ x = x - 6 \\ x = {x}^{2} - 12x + 36 \\ \\ x - {x}^{2} + 12 - 36 = 0 \\ \\ 13x - {x}^{2} - 36 = 0 \\ {x}^{2} - 13x + 36 = 0 \\ {x}^{2} - 4x - 9x + 36 = 0 \\ x \times (x - 4) - 9 \times (x - 4) = 0 \\ x = 4 \\ x = 9 \\ \sqrt{4} + 5 + 1 = 4 \\ \sqrt{9} + 5 + 1 = 9 \\8 = 4 \\ 9 = 9 \\ x = 9$