Question

розв'яжіть рівняння
√(x+1)=x-1​

Answer 1

Ответ:

$\sqrt{x + 1} = x - 1$

${ \sqrt{x + 1} }^{2} = (x - 1) ^{2}$

$x + 1 = {x}^{2} - 2x + 1$

$x = {x}^{2} - 2x$

$x - {x}^{2} + 2x = 0$

$3x - {x}^{2} = 0$

$x(3 - x) = 0$

$x = 0 \\ 3 - x = 0$

$3 - x = 0 \\ - x = - 3 \\ x = 3$

$x = 0 \\ x = 3$

$\sqrt{0 + 1} = 0 - 1 \\ \sqrt{3 + 1} = 3 - 1$

$\sqrt{0 + 1} = 0 - 1 \\ \sqrt{1} = 0 - 1 \\ 1 = - 1$

$\sqrt{3 + 1} = 3 - 1 \\ \sqrt{4} = 2 \\ 2 = 2$

$1 = - 1 \\ 2 = 2$

$x≠0 \\ x = 3$

$x = 3$