I believe that the question stem should read as follows:
Milovan wrote:If a and n are positive numbers, does 2(a^2x) = n ?
(1) a^x + 1/a^x = sqrt (n+2)
(2) x > 0
Remember the following identity:
(x+y)² = x² + 2xy + y²
Statement 1: a^x + 1/a^x = sqrt (n+2)
a^x + a^-x = √(n+2).
Squaring both sides, we get:
(a^x)² + 2(a^x)(a^-x) + (a^-x)² = n+2
a^2x + 2(a�) + a^(-2x) = n+2
a^2x + a^(-2x) = n.
Substituting a^2x + a^(-2x) = n into the question stem --
Does 2(a^2x) = n? -- we get:
Does 2(a^2x) = a^2x + a^(-2x)?
Does a^2x = a^(-2x)?
Does a^4x = 1?
Case 1: If a=1 and x=1, the answer is YES.
Case 2: If a=2 and x=1, the answer is NO.
INSUFFICIENT.
Cases 1 and 2 also satisfy statement 2.
Thus, even when the statements are combined, the answer to the question stem can be YES or NO.
The correct answer is
E.
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