<p>If (a+b)^1/2 = (a-b)^-1/2, which of the following must be true?
A) b = 0
B) a+b = 1
C) a -b = 1
D) a^2 + b^2 = 1
E) a^2 - b^2 = 1</p>
<p>(a+b) ^ 1/2 is the same as root (a+b)
(a-b) ^ -1/2 is the same as 1 / ( root (a-b) )</p>
<p>so therefor : root (A+B) = 1 / (root (a-b ) )
^2 everything
a+b = 1 / a-b
so therefor (a+b) (a-b) = 1
a^2 - b^2 = 1</p>
<p>In general, to get rid of square roots (or 1/2 powers) square both sides of the equation.</p>
<p>To get rid of denominators (or negative exponents) multiply both sides of the equation by each denominator (or better, the LCD).</p>
<p>Thank you to both posters above for your guidance.</p>