Call the expression X.
Squaring yields 4-(4+X)^.5, so
X^2= 4-(4+X)^.5. Squaring again and rearranging yields:
X^4-8X^2-X+12=0
Try factoring and allocating an X^2 to each (?) and last elements of each have to multiply to 12, correct ?
(X^2...-4)(X^2...-3)
Using minuses above because seems right to generate a negative 8X^2
So far, X^4-7X^2+12. Need a negative X, for sure, and another -X^2.
The -X^2 has to be a +X and a -X multiplied, but which side do each go ?
Let's just try:
(X^2-X-4)(X^2+X-3), which upon expansion does yield our original expression.
One or both of the above equals 0, so:
X= (1+/- (17)^.5)/2 perhaps?
Well, 1<X<2 by inspecting up top, and this expression >2.5, so it must be:
X^2+X-3=0, or
X= (-1+/- (13)^.5)/2
Since X>0, X=((13)^.5)-1)/2
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