## ឯកសារបំប៉នគណិតវិទ្យាថ្នាក់ទី ១២ ខែមករា 28, 2011

Posted by តារារស្មី in Uncategorized.

## មតិ»

1. chhinsopheara - ខែ​កុម្ភៈ 3, 2011

why is the book isnot answer i want see answer.how can i see?

តារារស្មី - ខែ​កុម្ភៈ 5, 2011

because solutions were given during training… and there’s no people responsible for typing the solutions yet… srr

phal sovannrath - ខែ​កុម្ភៈ 4, 2012

i think most of the exercise in this book are sold out on the market already………..by cmg……..

2. Chea touchsorady - ខែ​កុម្ភៈ 9, 2011

If I have some exercises want you to solve how can i post it. I have an exercise that i can’t solve it. I bought your book call but your solution i can’t understand at all.

smey - ខែ​កុម្ភៈ 20, 2011

just post in comment here…

3. suytry_ky_007 - ខែ​កុម្ភៈ 17, 2011

Hello! I want to join group CMG. How can I join?

smey - ខែ​កុម្ភៈ 20, 2011
4. Chea touchsorady - ខែ​មីនា 3, 2011

Can help me to solve this exercise
Calculate f(19) we know that f(1)=o and f(m+n)=f(m)+f(n)+3(4mn-1);m;n for Z

Choeng hor leang - ខែ​មីនា 13, 2011

For this exercise as my idea I have two solutions but I don’t know it right or wrong:
Solution 1
We have :
f(1)=0
f (m+n) = f (m) + f(n) + 3(4mn – 1)

Take m = n = 1
f (1+1) = f (1) + f(1) + 3(4 – 1)
f (2) = 9 (1)

f (1+2) = f (1) + f(2) + 3(8 – 1)
f (3) = 9 + 21 = 30 (2)

f (2+2) = f (2) + f (2) + 3(16 – 1)
f (4) = 2f (2) + 45
By (1)
f (4) = 18 + 45 = 63 (3)

f(5) = f(2) + f(3) + 3(24 – 1)
By (1) and (2)
f(5) = 9 + 30 + 69 = 108 (4)

Anyway We have

f(19) = f(10 + 9) = f(10) + f(9) + 3(360 – 1) (5)

But f(10) = f(5 +5) = f(5) + f(5) + 3(100 – 1)
By (4) f(10) = 108 + 108 + 3(100 – 1) = 513 (6)

f(9)= f(5 +4) = f(5) + f(4) + 3(80 – 1)
By (3) and (4)
f(9) = 63 + 108 +3(80 – 1) = 408 (7)

Take (6) and (7) put in (5)
f(19) = 513 + 408 + 3(360 – 1) = 1998

THAS: f(19) = 1998
Solution 2

We have
f(19) = f(18) +f(1) + 3(72 – 1)
But f(18) = f(9) + f(9) + 3(324 – 1)
In solution 1 we have f(9) = 408
f(18) = 408 + 408 +969 = 1785
Than f(19) = 1785 + 0 + 213 = 1998
THAS: f(19) = 1998

As these 2 solutions they show that however we still have 1 answer.
This just my solution, If there have the mistake Please tell me pong.
Email: C_H_leang@yahoo.com

5. leang - ខែ​មីនា 12, 2011

The books you made is very important to me because it can help me to find the solution of some exercises. i think you sould try to make a new more book for some student searching with it.

smey - ខែសីហា 30, 2011

Thank you we will do our best

6. Peng P - ខែ​មេសា 10, 2011

I enjoy ur book so much but I difficult to understand, so can u detail than before? I hope u can. Can u share me some experiences that make me learn math and Science subjects to be great than before?

7. Peng P - ខែ​មេសា 10, 2011

Mr. Leang if I have question can I ask u on mail? I hope u permit me.
I think u math smart student, so can show me techniques or experiences to learn math and Science subject to be great that before. Thanks…If u can, share me some math or other exercises…

8. Lynne - ខែវិច្ឆិកា 22, 2011

សួស្តីបងៗ ប្រសិនបើខ្ញុំមានចម្ងល់លំហាត់គណិតតើអាចសួរទៅកាន់បងៗបានេទ?

9. ឃាង - ខែធ្នូ 22, 2011

សូមជួយដោះស្រាយលំហាត់”ត្រីកោណ ABCមានរង្វាស់ជ្រុុងa b c មានទំនាក់ទំនង ។បង្ហាញថា Aជាមុំស្រួច។

10. ឃាង - ខែធ្នូ 22, 2011

មានទំនាក់ទំនងa3=b3+c3

Yeun sayon - ខែធ្នូ 24, 2011

☆。★。☆。★
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* good night *
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11. suyheimmenglang - ខែ​ឧសភា 24, 2012

i interest this book .tell me pong way i put my photo in my profile .

12. ចុច វិជ្ជា - ខែតុលា 2, 2013

ខ្ញុំបានអានសៀវភៅែដលបងៗបានចងក្រង វាពិតជាល្អហើយខ្ញុំចូលចិត្តវាយ៉ាងខ្លាំង។