Question
If $${3^{\frac{x}{2}}} + {2^x} > 25$$ then the solution set is
A.
$$R$$
B.
$$\left( {2, + \infty } \right)$$
C.
$$\left( {4, + \infty } \right)$$
D.
None of these
Answer :
$$\left( {4, + \infty } \right)$$
Solution :
By trial, $${3^{\frac{x}{2}}} + {2^x} \leqslant 25\,\,{\text{for }}x = 1,2,3,4.\,\,{\text{But }}{3^{\frac{x}{2}}} + {2^x} > 25\,\,{\text{for }}x > 4.$$