How do you solve the equation #sqrtt+sqrt(1+t)-4=0# to find the zeros of the given function?

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Answer 1 · 2016-12-17T09:58:36

#t = (15/8)^2#

First we establish the feasible solutions. They must obey:

From #sqrt(t)->t ge 0# and from #sqrt(1+t)->1+t ge 0# so
#t ge 0#

Now grouping

#sqrt(t+1) = 4 - sqrt(t)#

and squaring

#t+1=16-8sqrt(t)+t# simplifying

#8sqrt(t)=15# so

#t = (15/8)^2 > 0#

so the solution is feasible