Question

Resolva a equação irracional $\sf \sqrt{x - 1} = 3 -x .$

Answer 1

$\sqrt{x - 1} = 3 - x \\ x - 1 = 9 - 6x + {x}^{2} \\ x - 1 - 9 + 6x - {x}^{2} = 0 \\ 7x - 10 - {x}^{2} = 0 \\ - {x}^{2} + 7x - 10 = 0 \\ {x}^{2} - 7x + 10 = 0 \\ {x}^{2} - 2x - 5x + 10 = 0 \\ x \times (x - 2) - 5(x - 2) = 0 \\ (x - 2) \times (x - 5) = 0 \\ x - 2 = 0 \\ x - 5 = 0 \\ x = 2 \\ x = 5 \\ \sqrt{2 - 1} = 3 - 2 \\ \sqrt{5 - 1} = 3 - 5 \\ 1 = 1 \\ 2 = - 2 \\ x = 2 \\ x≠5 \\ x = 2$