Question

Решите уравнение √(7-3x)=1-x

Answer 1

$\sqrt{(7 - 3x)} = 1 - x$

$7 - 3x = 1 - 2x + x {}^{2}$

$7 - 3x - 1 + 2x - x {}^{2} = 0$

$6 - x - x {}^{2} = 0$

$- x {}^{2} - x + 6 = 0$

$x {}^{2} + x - 6 = 0$

$x {}^{2} + 3x - 2x - 6 = 0$

$x \times (x + 3) - 2(x + 3) = 0$

$(x + 3) \times (x - 2) = 0$

$x + 3 = 0 \\ x - 2 = 0$

$x = - 3 \\ x = 2$

$\sqrt{7 - 3 \times ( - 3)} = 1 - ( - 3) \\ \sqrt{7 - 3 \times 2} = 1 - 2$

$4 = 4 \\ 1 = - 1$

$x = - 3 \\ x≠2$

$x = - 3$