<p>How would one go about solving this math question:</p>
<p>(a + b)^(1/2) = (a - b)^(-1/2) , which of the following must be true?</p>
<p>A.) b = 0
B.) a + b = 1
c.) a - b = 1
D.) a² + b² = 1
E.) a² - b² = 1</p>
<p>Im totally lost on how to solve this, any help is much appreciated :)</p>
<p>Raising something to (1/2) means taking the square root.
As for the right side of the equal sign, you must make use of this rule:</p>
<p>a^-x = 1/(a^x)
And since x in this case is 1/2, you’re going to get:</p>
<p>(a + b)^(-1/2) = 1/((a + b)^(1/2)), or, since 1/2 is square root, this also means 1/square root of (a + b)</p>
<p>So your total equation is
square root of (a + b) = 1/(square root of a + b)</p>
<p>Multiply both sides by square root of (a + b) to get
(square root of a + b)^2 = 1
Remember, square root of (a + b) is the same as (a + b)^(1/2), so:
((a + b)^(1/2))^2 = 1
(a + b)^1 = 1
a + b = 1</p>
<p>@Yamster you wrote the question incorrectly, its (a+b)^(1/2) = (a-b)^(-1/2) notice the negative sign on the exponent on the right side of the equation and also note that it is a MINUS b on the right side of the equation. And the answer is (E), but im still not sure of how they got (E). Thanks for trying to explain it though.</p>
<p>I figured it out 
</p>
<p>heres solution for anyone intrested:</p>
<p>(a + b)^1/2 = (a - b)^(-1/2)
<em>Square both sides</em>
(a + b) = (a - b)^-1
<em>re-write</em>
(a + b) = 1/(a-b)
<em>multiply both sides by (a-b)</em>
(a + b)(a - b) = 1
<em>FOIL</em>
a² - b² = 1
Choice (E)!</p>