<p>I tried searching but I don't think the search engine handles exponents too well</p>
<p>If (a+b)^.5 = (a-b)^-.5 which must be true:</p>
<p>b = 0
a + b = 1
a - b = 1
a^2 + b^2 = 1
a^2 - b^2 = 1</p>
<p>(a+b)^1/2 = (a-b)^-1/2</p>
<p>(a+b)^1/2 = 1/(a-b)^1/2</p>
<p>Square both sides: a+b = 1/(a-b)</p>
<p>Multiply both sides by (a-b): (a-b)(a+b) = 1</p>
<p>Difference of squares: a^2-b^2 = 1</p>
<p>Tough problem but I finally figured it out.</p>
<p>(a+b)^(1/2) = (a-b)^(-1/2)
(a+b) = 1/(a-b)
(a+b)(a-b) = 1
a^2 - b^2 = 1</p>