be real numbers . Prove that
![$$-\frac{1}{30}\leq \frac{ab+a+b+4}{(a^2+a+5)(b^2+b+5)}\leq \frac{64+24\sqrt[3] 6+9\sqrt[3] {36} }{700} $$](http://latex.artofproblemsolving.com/d/a/2/da21df4e61f8934aa355a68cae4d3e274c176741.png)
![$\color[rgb]{0.35,0.35,0.35}v_1=2$](http://latex.artofproblemsolving.com/2/0/4/204b13717fb1dec258e4917232ca9c96344031d2.png)
,![$\color[rgb]{0.35,0.35,0.35}v_2=4$](http://latex.artofproblemsolving.com/b/c/2/bc24e9589aaf75cb848e9fddeef43fb7a6fea2c3.png)
and ![$\color[rgb]{0.35,0.35,0.35} v_{n+1}=3v_n-v_{n-1}$](http://latex.artofproblemsolving.com/8/7/3/8734d09c683e906771abf049d89b273196175585.png)
,![$\color[rgb]{0.35,0.35,0.35}v_n=2F_{2n-1}$](http://latex.artofproblemsolving.com/b/1/e/b1efbac9eef93c5649dab70be54ae2286ca5b2f0.png)
,![$\color[rgb]{0.35,0.35,0.35}F_n$](http://latex.artofproblemsolving.com/0/2/5/025c95f57f5317da3d9739c1620448d8f7cf4e47.png)
are the Fibonacci numbers.
be real numbers such that 
Prove that
Let 
Prove that
Y by Mango247
The side edges 
of the pyramid 
are equal to 
, and 
, respectively the base of the ABC is a regular triangle. It is known that the area of the lateral faces of the pyramid are equal to each other. Find the volume of the pyramid .
of the pyramid 
are equal to 
, and 
, respectively the base of the ABC is a regular triangle. It is known that the area of the lateral faces of the pyramid are equal to each other. Find the volume of the pyramid .
has length 
.
has sides 
,
has sides 
,
for convenience), we have 
,
,
.
,
.
times the square of the volume) of this purported tetrahedron to check if it positive. However, 
)
