maxx1234 wrote:
If \(x^2 + \frac{9}{x^2} = 31\), what is the value of \(x - \frac{3}{x}\)?
A. 36
B. 25
C. 9
D. 5
E. 3
Let \(a\) = the correct answer.
\(x - \frac{3}{x}=a\)
Since \((m-n)^2 = m^2 + n^2 - 2mn\), squaring both sides yields the following:
\((x - \frac{3}{x})^2=a^2\)
\(x^2 - \frac{9}{x^2} - 2(x)(\frac{3}{x})=a^2\)
\(x^2 - \frac{9}{x^2} - 6=a^2\)Substituting \(x^2 + \frac{9}{x^2} = 31\) into the resulting blue equation, we get:
\(31 - 6=a^2\)
\(25 = a^2\)
±\(5=a\)
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