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If sqrt(2*sqrt(2 - t)) = 7 - t, then find t.

 Dec 10, 2021
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sqrt(2*sqrt(2 - t)) = 7 - t

 

\(\sqrt{2*\sqrt{2 - t}} = 7 - t\\ 2*\sqrt{2 - t} = t^2-14t+49\\ \sqrt{2 - t} =\frac{ t^2-14t+49}{2}\\ 2 - t =\frac{( t^2-14t+49)( t^2-14t+49)}{4}\\ 8 - 4t =( t^2-14t+49)( t^2-14t+49)\\ 0 =( t^2-14t+49)( t^2-14t+49)+4t-8 \)

 

\(0=2401 - 1372 t + 294 t^2 - 28 t^3 + t^4+4t-8\\ 0=t^4 - 28 t^3 + 294 t^2 - 1368 t + 2393\)

 

Wolfram alpha says no real solutions.

You do need to check my algebra though. (for careless errors)

 

 

 

LaTex:

\sqrt{2*\sqrt{2 - t}} = 7 - t\\

2*\sqrt{2 - t} = t^2-14t+49\\
\sqrt{2 - t} =\frac{ t^2-14t+49}{2}\\

2 - t =\frac{( t^2-14t+49)( t^2-14t+49)}{4}\\
8 - 4t =( t^2-14t+49)( t^2-14t+49)\\

0 =( t^2-14t+49)( t^2-14t+49)+4t-8

 Dec 10, 2021

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