How do you solve $sqrt( t - 9) - sqrtt = 3$ ?

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Answer 1 · 2018-03-14T21:46:47

See below...

First we need to manipulate the equation to get $t$ by itself.

$sqrt(t-9)-sqrt(t)=3$
$sqrt(t-9)=3+sqrt(t)$

Now let's expand both sides to remove the root.

$sqrt(t-9)^2=(3+sqrt(t))^2$
$t-9=9+6sqrt(t)+t$

Now by manipulating this equation we can solve for $t$

$t-18=6sqrt(t)+t$
$-18=6sqrt(t)$
$(-18)^2 = (6sqrt(t))2$
$324=36t$
$t=9$

Now we have to verify the solution by subbing $t$ back into the original equation.

$sqrt(9-9) - sqrt(9) = 3$
$0-3 =3$
$-3=3$

This is false, $therefore$ no actual solutions.

How do you solve sqrt( t - 9) - sqrtt = 3sqrt( t - 9) - sqrtt = 3?