Search found 190 matches
- Wed Feb 29, 2012 12:54 am
- Forum: Geometry
- Topic: AN INTERESTING TRIGONOMETRY PROBLEM
- Replies: 2
- Views: 1928
AN INTERESTING TRIGONOMETRY PROBLEM
Prove that for a triangle ABC , $ \frac{a+b}{c}=\frac{cos\frac{A-B}{2}}{sin\frac{C}{2}} $.
- Tue Feb 28, 2012 12:19 am
- Forum: Number Theory
- Topic: FIND OUT THE SMALLEST 2 VALUES(SELF-MADE)
- Replies: 3
- Views: 2746
Re: FIND OUT THE SMALLEST 2 VALUES(SELF-MADE)
Correct ...Thanks .
- Tue Feb 28, 2012 12:15 am
- Forum: Geometry
- Topic: AN WONDERFUL PROPERTY
- Replies: 2
- Views: 2277
AN WONDERFUL PROPERTY
Let, ABC be a triangle & DEF is its medial triangle.Let, J is in-center of DEF . I,G,N are in-center, centroid & Nagel point of ABC respectively. Prove that ,GI,J,N are collinear .
- Mon Feb 27, 2012 2:29 am
- Forum: Algebra
- Topic: TRY TO DISPROVE,A QUESTION ABOUT POWER
- Replies: 1
- Views: 1805
TRY TO DISPROVE,A QUESTION ABOUT POWER
1 of my friend showed $ 1^0=1^1 $. Then, 1=0. But, I mentioned him wrong. I also showed $ 1^2= 1^3= 1^4 =... $ .But,it is not possible that ,2=3=4=5 =... .But, is it possible to disprove it rigorously ? Can I do it with the help of empty product concept ?? I need a very rigors logic so that we can e...
- Sun Feb 26, 2012 12:58 pm
- Forum: Higher Secondary Level
- Topic: বুঝি নাই-০১ :(
- Replies: 10
- Views: 8326
Re: বুঝি নাই-০১ :(
২য় টার জন্য bossদের সাহায্য চাইতেছি ।।
- Sun Feb 26, 2012 12:56 pm
- Forum: Higher Secondary Level
- Topic: বুঝি নাই-০১ :(
- Replies: 10
- Views: 8326
Re: বুঝি নাই-০১ :(
২ টা আমিও অনেক বার পড়ছি ।। এবং অনেক বারই মাথার উপর দিয়ে গেছে ...
ABOUT HCl
Let, we have taken $ 10^{-9} $ M HCl. now, $ pH=-(log [H^{+}]).=-(log 10^{-9})=-(-9)log 10=9 $ . & We know that pH greater than 7 are base. but, HCl is acid ?? so, what is the problem ??
- Sun Feb 26, 2012 5:53 am
- Forum: Algebra
- Topic: MODULUS OF COMPLEX NUMBER
- Replies: 2
- Views: 2878
MODULUS OF COMPLEX NUMBER
Let z ∈ C∗ such that, $ |z^3 + \frac{1}{z^3}|≤ 2. $ Prove that $ |z + \frac{1}{z}|≤ 2. $
- Sun Feb 26, 2012 4:31 am
- Forum: Algebra
- Topic: 1999 Romanian Mathematical Olympiad – Final Round
- Replies: 2
- Views: 2395
1999 Romanian Mathematical Olympiad – Final Round
Let p and q be complex numbers with $ q\neq 0.$ Prove that if the roots of the
quadratic equation $x^2 + px + q^2 = 0 $ have the same absolute value, then
p/q is a real number.
quadratic equation $x^2 + px + q^2 = 0 $ have the same absolute value, then
p/q is a real number.
- Sun Feb 26, 2012 4:28 am
- Forum: Algebra
- Topic: AN INTERESTING PROBLEM WITH COMPLEX NUMBER
- Replies: 1
- Views: 1739
AN INTERESTING PROBLEM WITH COMPLEX NUMBER
Let a, b, c be distinct nonzero complex numbers with |a| = |b| = |c|.
Prove that if a root of the equation $az^2 + bz + c = 0 $ has modulus equal to 1,then $b^2 = ac. $.
Prove that if a root of the equation $az^2 + bz + c = 0 $ has modulus equal to 1,then $b^2 = ac. $.