jump to navigation

សប្បាយៗ​ជាមួយ​គណិតវិទ្យា ខែកក្កដា 18, 2009

Posted by ពិសិដ្ឋ in គណិតវិទ្យា, សំណើច.
Tags:
trackback

មតិ»

1. lim phalkun - ខែកញ្ញា 17, 2009

Problem
u1 = u2= 1 and un+2 = 2 un+1 – 2un for all n =1 , 2 , 3 ,
Find Un ?

ឆ្លើយតប
2. lim phalkun - ខែកញ្ញា 17, 2009

Prolem 1

let a > b > c > 1 and abc +a+b+c = ab+bc+ca +2010
Prove that :
ln(a-1)+ln(b-1)+ln(c-1)=ln2009

Problem 2

Let ABC be a triangle and 0 < A , B , C < 90 .
a/ prove that :
tanA+tanB+tanC = tanA tanB tanC
b/ find min { tanA+tanB+tanC } ?

Problem 3

Prove that :
tan3x – tan2x – tanx = tanx tan2x tan3x

Problem 4

Compute :
A = (1+tan1)(1+tan2)(1+tan3)….(1+tan44)
B= (1-tan1)(1-tan2)(1-tan3)…..(1-tan44)

Problem 5

Such that :
sina+7sinb=4(sinc+2sind) and cosa+7cosb=4(cosc+2cosd)
Prove that 2 cos ( a – d ) = 7 cos ( b – d )

ឆ្លើយតប
3. Math today - ខែកញ្ញា 18, 2009

Problem
Find the sum :

S=sinx+sin2x+sin3x+….+sin(nx)
C=cosx+cos2x+cos3x+……+cos(nx)

Remarque
set Z = S + i C.

ឆ្លើយតប
4. Math today - ខែកញ្ញា 18, 2009

Problem

Compute :

S=tanxtan2x+tan2xtan3x+tan3xtan4x+…..+tan(nx)tan(n+1)x

Remarque
Use : tan(a-b) (1-tanatanb) = tana-tanb and take a=nx and b=(n+1)x .

ឆ្លើយតប
5. លឹម ផល្គុន​​ - ខែកញ្ញា 18, 2009

លំហាត់
១-ដោះស្រាយសមីការ
​​​ ​​ sinx+√3 cosx=√2
២-គេឲ្យអនុគមន៍​ f(x)=x^2+x+1
ក-ចូរបង្ហាញថា​​​ f(x^2 )=f(x)f(-x)
ខ-គណនា​​​​ P(n)=f(-7).f(-49)…..f(-7^2^k )

ឆ្លើយតប

បញ្ចេញមតិ