SOLUTION: Find all real values of t that satisfy the equation (t^2 - 13)^2 = 144 + 8t^2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find all real values of t that satisfy the equation (t^2 - 13)^2 = 144 + 8t^2      Log On


   

Question 1209148: Find all real values of t that satisfy the equation
(t^2 - 13)^2 = 144 + 8t^2
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Instead of doing it for you, I'll do one exactly like it so you
can do yours by using it as a model to go by following through 
the same steps:

Find all real values of t that satisfy the equation
(t^2 - 12)^2 = 140 + 6t^2

%28t%5E2+-+12%29%5E2+=+140+%2B+6t%5E2

%28t%5E2+-+12%29%5E2+=+140+%2B+6t%5E2

t%5E4-24t%5E2%2B144=140%2B6t%5E2

t%5E4-30t%5E2%2B4=0

t%5E2+=+%28-%28-30%29+%2B-+sqrt%28%28-30%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29+ 

t%5E2+=+%2830+%2B-+sqrt%28900-16+%29%29%2F2+ 

t%5E2+=+%2830+%2B-+sqrt%284%2A221%29%29%2F2+ 

t%5E2+=+%2830+%2B-+2sqrt%28221%29%29%2F2+

t%5E2+=+15+%2B-+sqrt%28221%29+ 

t=%22%22+%2B-+sqrt%2815+%2B-sqrt%28221%29%29

So there are 4 solutions, for the 4 possible combinations of signs

(1) t=%22%22+%2B+sqrt%2815+%2Bsqrt%28221%29%29

(2) t=%22%22+%2B+sqrt%2815+-sqrt%28221%29%29

(3) t=%22%22+-+sqrt%2815+%2Bsqrt%28221%29%29

(4) t=%22%22+-+sqrt%2815+-sqrt%28221%29%29 

Now do yours the exact same way.  Your answer will also have 
similar answers, with a square root inside a square root.

Edwin