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

1 Answer
LucaGasparro
Mar 14, 2018

See below...

Explanation:

First we need to manipulate the equation to get tt by itself.

sqrt(t-9)-sqrt(t)=3√t−9−√t=3
sqrt(t-9)=3+sqrt(t)√t−9=3+√t

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

sqrt(t-9)^2=(3+sqrt(t))^2√t−92=(3+√t)2
t-9=9+6sqrt(t)+tt−9=9+6√t+t

Now by manipulating this equation we can solve for tt

t-18=6sqrt(t)+tt−18=6√t+t
-18=6sqrt(t)−18=6√t
(-18)^2 = (6sqrt(t))2(−18)2=(6√t)2
324=36t324=36t
t=9t=9

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

sqrt(9-9) - sqrt(9) = 3√9−9−√9=3
0-3 =30−3=3
-3=3−3=3

This is false, therefore no actual solutions.

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