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#301 Re: Help Me ! » Find real solutions » 2007-11-02 07:45:06

We have

.
Adding the first two equations and substracting the third, we have:



  (1)

If


Then

In the same way if one of the others two factors from (1) is 0

#302 Help Me ! » acute angles a and b » 2007-11-02 00:29:49

tony123
Replies: 1

Find the acute angles a and b that satisfy the following simultaneous equations:

2sin 2b =3 sin 2a

tan b =3 tan a

#303 Help Me ! » divisible by 101 » 2007-11-02 00:22:58

tony123
Replies: 1

Find the positive integers n for which n^3+1 and n^2-1 are both divisible by 101

#304 Help Me ! » how many » 2007-11-01 14:04:38

tony123
Replies: 3

how many non overlapping 2 by 2 squares will fit into a circle with radies 8

#307 Help Me ! » Find real solutions » 2007-10-21 07:07:21

tony123
Replies: 8

Find real solutions of the system

sin x + 2 sin(x+y+z) = 0,
sin y + 3 sin(x+y+z) = 0,
sin z + 4 sin(x+y+z) = 0.

#308 Help Me ! » inequality » 2007-10-21 06:55:18

tony123
Replies: 1

Prove that for every natural n the following inequality is valid:

|sin 1| + |sin 2| + |sin(3n-1)| + |sin(3n)| > 8n/5.

#310 Help Me ! » sum Series » 2007-10-15 22:34:17

tony123
Replies: 1

sum Series
1/(log 2) + 1/(log 2)(log 3) + 1/(log 2)(log 3)(log 4) + ...



1/(sin²1)² + 1/(sin²1+sin²2)² + 1/(sin²1+sin²2+sin²3)² + 1/(sin²1+sin²2+sin²3+sin²4)² + .

#311 Help Me ! » 3,3,7,7 =24 » 2007-10-07 21:35:09

tony123
Replies: 4

these four numbers must equal 24          3,3,7,7  you can use  add. sub. mul. div.  each number must only be used once

#312 Help Me ! » Sum of Powers » 2007-10-05 22:24:20

tony123
Replies: 2

Find the last decimal digit of the sum 1^1 + 2^2 + 3^3 + ... + 2001^2001

#313 Help Me ! » not isosceles » 2007-10-05 09:30:45

tony123
Replies: 0

Triangle ABC is not isosceles. The incenter is I, the excenter is O. The incircle touches the sides BC, CA, AB at points D, E, F, respectively. Lines FD and AC intersect at P, lines DE and AB intersect at Q. The midpoints of segments EP amd FQ are M and N, respectively. Prove that MN and OI are perpendicular.

#314 Re: Help Me ! » solve in R » 2007-10-03 22:04:14

(4,9).is the only answer but how

#315 Help Me ! » A circle with center O » 2007-10-03 10:29:03

tony123
Replies: 3

A circle with center O and radius 1 cm rolls around the inside of a triangle whose sides are 6, 8, and 10 cm, always touching one or more of the sides as it rolls. How far does O travel in one complete circuit?

#316 Help Me ! » n positive integers » 2007-10-02 05:18:36

tony123
Replies: 1

n positive integers

prove

#318 Re: Help Me ! » prove tri » 2007-09-26 21:06:29

JaneFairfax you are jenus

using the addition formula for tangents, we have

.

Now obviously, for t = pi/7, 2pi/7, ..., 7pi/7, we have

. and thus, these are the roots of

Put differently,

.  are the roots of

.

Since

. ,
we may divide by x to leave an equation of
which
.
  are the roots:

.

#319 Re: Help Me ! » prove tri » 2007-09-26 20:59:02

JaneFairfax you are jenus

using the addition formula for tangents, we have

.

Now obviously, for t =\ pi/7, 2\pi/7, ..., 7\pi/7, we have

. and thus, these are the roots of

Put differently,

.  are the roots of

.

Since

. , we may divide by x to leave an equation of which
.  are the roots:

.

#321 Help Me ! » divisible by 10 » 2007-09-22 20:20:03

tony123
Replies: 4

a,b,c,d integers, a+b+c+d=0
prove

a^5+b^5+c^5+d^5 divisible by 10

#322 Help Me ! » prove tri » 2007-09-22 05:18:22

tony123
Replies: 14

cos (-89)+cos (-87) +.......+cos87 +cos 89 =csc 1


tan²(pi/7) +tan²(2pi/7) +tan²(3pi/7) =21

#323 Help Me ! » solve in R » 2007-09-13 20:07:13

tony123
Replies: 1

solve
x + y^2 + z^3 = 3
y + z^2 + x^3 = 3
z + x^2 + y^3 = 3

#325 Help Me ! » sequence » 2007-09-08 04:28:40

tony123
Replies: 2


sequence 20,30,70,180,470,1230,...
find all natural numbers
such that
is  a perfect squer

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