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

Dec 17, 2016

$t = {\left(\frac{15}{8}\right)}^{2}$

#### Explanation:

First we establish the feasible solutions. They must obey:

From $\sqrt{t} \to t \ge 0$ and from $\sqrt{1 + t} \to 1 + t \ge 0$ so
$t \ge 0$

Now grouping

$\sqrt{t + 1} = 4 - \sqrt{t}$

and squaring

$t + 1 = 16 - 8 \sqrt{t} + t$ simplifying

$8 \sqrt{t} = 15$ so

$t = {\left(\frac{15}{8}\right)}^{2} > 0$

so the solution is feasible