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.