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 Soumik's messages in the community 1 2 3 ... 62 63 64 GO Go to Page...
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 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
try out jenson's inequality
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
Post the entire qsn.
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

No matter in whichever pattern u choose, the nos. shall always add upto 260.

There's a wonderful proof for this. Try it else I shall post it.

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

 Discussion Forums -> This Post 2 points    (0    in 1 votes )   [?]

Reflect the cosine graph about the origin to get that of -cosx....shift it downwards bmg times, and shift the sinx graph upwards mg times, now superimpose them strecthing it k times.....Hopefully got it now...

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

This is the graph of the above function, so even though  becomes integer for 2 values of x other than 0, it posses only 2 roots...

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 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

If [x] represents my frac part of x, then the above exp takes an integral value at [x]=0.8 as well......What about that....

1)

that gives xyz can have a max of 5.....thus we need to check for (2,1,1), (3,1,1), (4,1,1), (5,1,1) & (2,2,1)....

Thus no solutions....

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

But how does Pole-strength become halved in 2nd case?

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Do there exists a point equidistant from the set of points represented by the above exp ?

 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]

Consider the situation shown...

The eqn is

b is the coefficient of friction,

When

So eqn becomes that of a sraight line...

Later on,

Hpefully u can do this graph, if u still face prob, nudge me, I'll be there for help again!

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Edit :- Limits are from -pi to pi

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Is it not a std fact that extremes of the trig values occur at x=y=z=60 deg....

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

The qsn asks us to determine the no of reals, not necessarily the reals satisfying the above eqn....

S the graph turns out as a compressed parabola , and the line y=16, as the min value of f(x)=(6-x)4+(8-x)4 turns out to be less than that....

 Discussion Forums -> This Post 2 points    (0    in 1 votes )   [?]

Just an intuition....

Check for the derivative of f(x)=x2+7x-13....

f'(x)=2x+7, g'(x)=2x-3....

Clearly from the derivatives, f(x) becomes steeper, meaning after both the parabolas cross the X-axis, f(x)>g(x), while the opposite happens when they are below the X-axis.....

Will this do?

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Well, I played up my part as an idiot.....I proved no soln exists for xy+yz+zx=5xyz.....and not 5(xy+yz+zx)=xyz......

In fact there are finitely many solutions, (more than 8).....

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

@ Abhinav, according to the qsn, x,y,z are naturals, since when did 1/15 become a natural no.....?

Rudra, go ahead with ur solution.....

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

For the first 1, D>0 meaning a<-1 or a>4.....Prod of roots >9 meaning a>-4, sum of roots >6 meaning a<-2, thus range = (-4,-2)

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

....................(1)          x>x1     y>y1          z>z1

Now observe

For proving this use the fact

together with (x,y,z)  ...(Try it, I shall give it if u can't).

This proved suffices the case for x=y=z=1, by virtue of (1) above...

Thus no solutions exist!

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