Question

√m+3 - √m-1=2
equação irracional

Answer 1

$\sqrt{m + 3} - \sqrt{m - 1} = 2 \\ ( \sqrt{m + 3} - \sqrt{m - 1} {)}^{2} = {2}^{2} \\ ( \sqrt{m + 3} {)}^{2} - 2 \times \sqrt{m + 3} \times \sqrt{m - 1} + ( \sqrt{m - 1} {)}^{2} = 4 \\ m + 3 - 2 \sqrt{(m + 3)(m - 1)} + m - 1 = 4 \\ 2m + 2 - 4 = 2 \sqrt{(m + 3)(m - 1)} \\ 2 \sqrt{ {m }^{2} + 2m - 3 } = 2m - 2 \\ \sqrt{ {m}^{2} +2m - 3 } = m - 1 \\ ( \sqrt{ {m}^{2} + 2m - 3} {)}^{2} = (m - 1 {)}^{2} \\ {m}^{2} + 2m - 3 = {m }^{2} - 2m + 1 \\ {m}^{2} - {m }^{2} + 2m + 2m - 3 - 1 = 0 \\ 4m - 4 = 0 \\ 4m = 4 \\ m = \frac{4}{4} \\ \boxed{m = 1}$