Respuesta:
[tex]\sqrt{x + 7} + \sqrt{x - 1} - 2 \sqrt{x + 2 } = 0 \\ \sqrt{x + 7} + \sqrt{x - 1} - 2 \sqrt{x + 2 } + 2 \sqrt{x + 2} = 0 + 2 \sqrt{x + 2} \\ \sqrt{x + 7} + \sqrt{x - 1} = 2 \sqrt{x + 2} \\ \\ (\sqrt{x + 7} + \sqrt{x - 1} {)}^{2} = 2x + 2 \sqrt{x + 7} \sqrt{x - 1} + 6 \\ (2 \sqrt{x + 2} {)}^{2} = 4x + 8\\ \\ 2x + 2 \sqrt{x + 7} \sqrt{x - 1} + 6 = 4x + 8 \\ 2x + 2 \sqrt{x + 7} \sqrt{x - 1} + 6 - 2x = 4x + 8 - 2x \\ 2 \sqrt{x + 7} \sqrt{x - 1} + 6 = 2x + 8 \\ 2 \sqrt{x + 7} \sqrt{x - 1} + 6 - 6 = 2x + 8 - 6 \\ 2 \sqrt{x + 7} \sqrt{x - 1} = 2x + 2 \\ \\ (2 \sqrt{x + 7} \sqrt{x - 1} {)}^{2} = 4 {x}^{2} + 24x - 28 \\ (2x + 2 {)}^{2} = 4 {x}^{2} + 8x + 4 \\ \\ 4 {x}^{2} + 24x - 28 = 4 {x}^{2} + 8x + 4 \\ x = 2[/tex]
