If sqrt(u) + sqrt(v) - sqrt(w) = 0, then find the value of (u+v-w)?

If sqrt(u) + sqrt(v) - sqrt(w) = 0, then find the value of (u+v-w).

1 Answer
Jul 17, 2018

See a solution process below:

Explanation:

First, solve for w

sqrt(u) + sqrt(v) - sqrt(w) = 0

sqrt(u) + sqrt(v) - sqrt(w) + sqrt(w) = 0 + sqrt(w)

sqrt(u) + sqrt(v) - 0 = sqrt(w)

sqrt(u) + sqrt(v) = sqrt(w)

(sqrt(u) + sqrt(v))^2 = (sqrt(w))^2

(sqrt(u))^2 + 2sqrt(u)sqrt(v) + (sqrt(v))^2 = w

u + 2sqrt(u)sqrt(v) + v = w

Substituting the left side of the equation for the w in the expression gives:

(u + v - w) becomes:

(u + v - (u + 2sqrt(u)sqrt(v) + v)) =>

(u + v - u - 2sqrt(u)sqrt(v) - v) =>

(u - u + v - v - 2sqrt(u)sqrt(v)) =>

(0 + 0 - 2sqrt(u)sqrt(v)) =>

-2sqrt(u)sqrt(v)