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

Question

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

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Answer 1 · 2018-07-17T17:50:45

See a solution process below:

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)#