The minimum value of $${4^x} + {4^{1 - x}},x \in R,$$ is
A.
2
B.
4
C.
1
D.
none of these
Answer :
4
Solution :
$${\text{AM}} \geqslant {\text{GM}}$$ for positive numbers. So, $$\frac{{{4^x} + \frac{4}{{{4^x}}}}}{2} \geqslant \sqrt {{4^x} \cdot \frac{4}{{{4^x}}}} = 2.$$
Releted MCQ Question on Algebra >> Sequences and Series
Releted Question 1
If $$x, y$$ and $$z$$ are $${p^{{\text{th}}}},{q^{{\text{th}}}}\,{\text{and }}{r^{{\text{th}}}}$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}{y^{z - x}}{z^{x - y}}$$ is equal to:
If $$a, b, c$$ are in G.P., then the equations $$a{x^2} + 2bx + c = 0$$ and $$d{x^2} + 2ex + f = 0$$ have a common root if $$\frac{d}{a},\frac{e}{b},\frac{f}{c}$$ are in-