Answer:
x = 146/25 = 5.84
Step-by-step explanation:
[tex] \sqrt{x - 1} + \sqrt{x + 2} = 5 [/tex]
[tex] \sqrt{x - 1} = 5 - \sqrt{x + 2} [/tex]
[tex] (\sqrt{x - 1})^2 = (5 - \sqrt{x + 2})^2 [/tex]
[tex] x - 1 = 25 - 10\sqrt{x + 2} + x + 2 [/tex]
[tex] 10\sqrt{x + 2} = 28 [/tex]
[tex] (10\sqrt{x + 2})^2 = (28)^2 [/tex]
[tex] 100(x + 2) = 784 [/tex]
[tex] 100x + 200 = 784 [/tex]
[tex] 100x = 584 [/tex]
[tex] x = \dfrac{584}{100} [/tex]
[tex] x = \dfrac{146}{25} [/tex]
Ahora, comprobamos nuestra respuesta.
[tex] \sqrt{\frac{146}{25} - 1} + \sqrt{\frac{146}{25} + 2} = 5 [/tex]
[tex] \sqrt{4.84} + \sqrt{7.84} = 5 [/tex]
[tex] 2.2 + 2.8 = 5 [/tex]
[tex] 5 = 5 [/tex]
Respuesta: x = 146/25 = 5.84
