quite tough
by hemangsarkar, Sep 10, 2012, 6:32 AM
Q) find the number of real solutions of -
solution :
$1 - 3^x - \frac{3^{-x}}{4} = 1- \left(3^x +\frac{3^{-x}}{4} \right) = 1 - \left(\left(3^{x/2} + \frac{3^{-x/2}}{2} \right)^2 - 2*3^{x/2} *\frac{3^{-x/2}}{2} \right) = 2 - \left(3^{x/2} + \frac{3^{-x/2}}{2} \right)^2 < 2$
so no real solutions.
solution :
$1 - 3^x - \frac{3^{-x}}{4} = 1- \left(3^x +\frac{3^{-x}}{4} \right) = 1 - \left(\left(3^{x/2} + \frac{3^{-x/2}}{2} \right)^2 - 2*3^{x/2} *\frac{3^{-x/2}}{2} \right) = 2 - \left(3^{x/2} + \frac{3^{-x/2}}{2} \right)^2 < 2$
so no real solutions.
November 2016
June 2016