<PRE><B>Question 164762</B>
{{{sqrt(26t+10) - 5sqrt(t)}}} = 1
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Add {{{5sqrt(t)}}} to both sides:
{{{sqrt(26t+10)}}} = {{{1 + 5sqrt(t)}}}
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Square both sides (FOIL the right side)
26t + 10 = 1 + {{{10sqrt(t)}}} + 25t
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Isolate the radical on the right
26t - 25t + 10 - 1 = {{{10sqrt(t)}}} 
:
t + 9 = {{{10sqrt(t)}}}
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Square both sides (FOIL the left)
t^2 + 18t + 81 = 100t
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Arrange as a quadratic equation:
t^2 + 18t - 100t + 81 = 0
:
t^2 - 82t + 81 = 0
Factors to:
(t-81)(t-1) = 0
Two solutions
t = 81, and t = 1
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Both solution should be checked in the original equation:
t=81
{{{sqrt(26(81)+10) - 5sqrt(81)}}} = 1
{{{sqrt(2106+10)}}} - 5 * 9 = 1
{{{sqrt(2116)}}} - 45 = 1
46 - 45 = 1; a good solution
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You can check x=1 solution</PRE>