<PRE><B>Question 765156</B>
[(11-x^2)^1/2]-[2/(11-x^2)^1/2]=1
let u = [(11-x^2)^1/2] and then we have
u^2 -2 = u and
u^2 -u -2 = 0, factor this
(u-2) * (u+1) = 0, so we have
=====================================================================
[(11-x^2)^1/2] = 2
square both sides
11 -x^2 = 4
multiply both sides of = by -1
x^2 -11 = -4
x^2 = 7
x = sqrt(7)
==================================================================
[(11-x^2)^1/2] = -1
square both sides
11 -x^2 = 1
multiply both sides of = by -1
x^2 -11 = -1
x^2 = 10
x = sqrt(10)
=====================================================================
now we substitute back in original equation to check
(11 -7)^1/2 - 2 / (11-7)^1/2 = 1
2 - (2 / 2) = 1
2 - 1 = 1
x = sqrt(7)  checks out
=======================================================
now for x = sqrt(10)
(11-10)^1/2 - 2 / (11-10)^1/2 = 1
1 -2/1 = -1
this does not check out
=========================================================
our answer is x = sqrt(7) = 7^1/2
==========================================================</PRE>