MathDB
x^3.3^(1/x^3) + 1/x^3.3^(x^3) = 6

Source: 0

April 23, 2009
geometrygeometric transformation

Problem Statement

How many real solutions does the equation x^{3} 3^{1/x^{3} } \plus{}\frac{1}{x^{3} } 3^{x^{3} } \equal{}6 have?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> Infinitely many<spanclass=latexbold>(E)</span> None<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ \text{Infinitely many} \qquad<span class='latex-bold'>(E)</span>\ \text{None}