How do you solve #sqrtx -sqrt(x-1) = 1?

Question

2259 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-18T03:26:23

$sqrt(x) - sqrt(x - 1) = 1$

$sqrt(x) = 1 + sqrt(x - 1)$

$(sqrt(x))^2 = (1 + sqrt(x - 1))^2$

$x = 1 + x - 1 + 2sqrt(x - 1)$

$0 = 2sqrt(x - 1)$

$(0)^2 = (2sqrt(x - 1))^2$

$0 = 4(x - 1)$

$0 = 4x - 4$

$4 = 4x$

$x = 1$

Therefore, ${x = 1}$ . Checking the solution back in the original equation we find it works.

Hopefully this helps!