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Algebra short-techniques-and-formulas [www.onlinebcs.com]
1.
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com আনায ই−ফুক ফা pdf রযডারযয Menu Bar এয View অনরি তে রিক করয Auto /Automatically Scroll অনরি রররক্ট করুন (অথফা যারয তমরে Ctrl + Shift + H )। এফায ↑ up Arrow ফা ↓ down Arrow তে রিক করয আনায ড়ায ুরফধা অনুারয স্ক্রর স্পীড রিক করয রনন। ( )( ) ( ) ( ) −−−−−(x) ⇛ ( ) − ⇛ . / . / − ( − ) − −−−−−(y) ⇛ ( − ) ⇛ . / . − / ( ) ( − ) ( ) [ ∵ (x) +(y)] ⇛ ( ) ( ) ( ) − ( − ) [ ∵ (x) − (y)] ⇛( ) ( − ) ⇛( − ) ( ) − ⇛ ( ) ( )
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com ( ) ⇛ ( ) − ( ) ( ) ( ) ( ) ( ) ( )( )( ) ( ) ( ) ( ) ⇛ ( ) − ( ) ( − ) − − ⇛ − ( − ) ( − ) − ( )( − − − ) ⇛ − ( ) *( − ) ( − ) ( − ) + ( − ) ( − ) ( − ) ( − )( − )( − ) − ( )( − ) ( )( − ) − ( − )( )
3.
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com যাররিরক উৎাদন রফরেলণ কযরে রর , ধ্রফ যার q ংখ্যারিরক এভন দুইরি উৎাদরক (a ও b )প্রকা কযরে রফ মায ভরি ফা তমাগপর x এয গ q (q= a+b) এয ভান। এফং গুণপর ধ্রফ যার r (r=a×b)এয ভান। ⇛ ( ) ( )( ) 1) q>0, r>0 রর ( )( ) 2) q<0, r>0 রর ( − )( − ) 3) q>0, r<0 রর a ও b এয ভরধয ফড়রি + ও ত ািরি – রফ। ( ) ( )( ) ( ) ( ) ( )( )( ) ( ) ( )( ) রর এয ভুরদ্বয় রফ x = -a , x = -b । এয ভূরদ্বয় α ও β রর,⇒ α + β − এফং α × β = ∴ ভীকযণ − (α β ) αβ ভীকযরণয এয ভূরদ্বয় √ 2 4 2 যাররক (x-m) যার দ্বাযা বাগ কয? এখ্ারন (x-m) তক এভন একরি যার দ্বাযা গুন কযরে রফ মারে গুণপররয প্রথভ যার এফং বাজ্য( ) এয প্রথভ যারয( ) ভান য় । এখ্ন তম যার দ্বাযা গুন কযা রয়র তরি বাগপরর ফরফ । এফং গুণপর বাজ্য এয রনরে ফররয় রফরয়াগ কযরে রফ। এবারফ মযায়ক্ররভ বাগ করয তমরে রফ ।
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com a× × × × … (n ংখ্যক a এয গুণপর ) ( ) √ √ √ ( √ ) √ √ √ ( ) ( ) . / ফা ( ) মরদ য় ⇒ ∴ √ মরদ য় ∴ x =y মরদ য় ∴
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com তক “ a রবরিক রগ n”ড়া য়। শুধু ধনাত্নক ংখ্যায রগারযদভ আর । ূনয ও ঋনাত্নক ংখ্যায রগারযদভ তনই। াধাযণ রগারযদরভয রবরি 10 ধযা য়। তফাঝারে তক তফাঝায়। রর x = ⇛ x = রর ⇛ × ⇛ × × × ( ) . / − √
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com অজ্ঞাে যার ভূরয ভান দ্বাযা একারধক মুগৎ রধ হ রর ,ভীকযণ ভূরক একরস ভীকযণ ফরর। এই ধযরণয অংক যীক্ষায় MCQ রারফ আরর , াভাধারনয তক্ষরস MCQ এয োযরি Answer Choice এ x ও y এয োযরজ্াড়া ভান তদওয়া থাকরফ। এখ্ন প্ররেযক তজ্াড়া ভান অথযাৎ x ও y এয ভান প্ররে তদওয়া দুরি ভীকযরণয তম তকান একরিরে(রম ভীকযণরি অরক্ষাক ৃ ে জ্) ফান। এফং তদখ্ুন তকান ভারনয জ্নয ভীকযণরি ূনয য়। তম ভারনয জ্নয ভীকযণরি ূনয রফ তই ভানরি অয ভীকযরণও ফররয় তদখ্ুন ূনয য় রকনা , মরদ তকাণ ভারনয জ্নয উবয় ভীকযণ ূনয য় োরর রিক উিয রফ তরি।
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com ক্ররভক ভান্তয ধাযাাঃ 1(First Term) ……………………n(Last Term) এই ধাযায় াধাযণ অন্তয (Common Difference) =Second term – first Term = 1 দংখ্যা (Number of Terms) = তল দ প্রথভ দ াধাযণ অন্তয + 1 ভরি (Sum of the Series) = তল দ প্রথভ দ × দংখ্যা = ( ) গড় (Avarage of the Series) = তল দ প্রথভ দ = a + (a+d) + (a+2d) ( d) …………………………… n এখ্ারন ধাযারিয , প্রথভ দ = a াধাযণ অন্তয d = রদ্বেীয় দ – প্রথভ দ দ ংখ্যা = n ∴ ধাযায েভ n দ (রল দ) (n− )d ⇛ n = তল দ − ধাযায n েভ রদয ভরি = * (n− )d+ … … … … এখ্ারন গুরনািয ধাযারিয, প্রথভ দ = a াধাযণ অনুাে r = রদ্বেীয় দ প্রথভ দ দ ংখ্যা = n ধাযায n েভ দ = ×
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com r >0 ফা 1 অথযাৎ অনুাে r ধনাত্নক ূনয ংখ্যা রর, ধাযায n েভ রদয ভরি × r < 0 ফা 1 অথযাৎ অনুাে r ঋনাত্নক ফা বগ্াং (.1 -.9 )ংখ্যা রর, ধাযায n েভ রদয ভরি × মখ্ন -1<r<1 রর , এফং n→ রর ধাযায n েভ রদয ভরি ধাযায তমাগপর ফা ভরি = ধাযারে রদয ংখ্যা = n ধাযায n েভ দ = তল দ 1 ……………… n ⇛ = ( ) 1 5 7 ……………… ( − ) েভ দ তল দ ⇛ = (দংখ্যা) = … … … … … ⇛ = × n(n-1)(2n+1) ( ) … … … … … … … ⇛ = − … … … … … … … … … ⇛ = ( ) = * ( ) +
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com 1, 4, 9, 16……………. ⇒ 5,∵ 5 ] 1 , 9 , 25, 49, 81 ………… ⇒ ,∵ 5 7 9 রফরজ্াড় ংখ্যা ] 9 36 81 144 …….. ⇒ 5,∵ ( ) ( ) ] 81, 27, …. 3, 1 ⇒ 9 ,∵ ] 1, 2, 3, 5, 8 , 13 , 21 , 34……. ⇒ 55[∵ তম তকাণ দ = োয ুরফযয দুরি রদয ভরি ] 8, 11, 17, 29, 53,….. ⇒ 101 [∵8, 8+(11-8),11+(17-11), …] 1, 3, 6, 10, 15, 21,…. ⇒ 28 [∵ 1,(1+2),(3+3),(6+4), (10+5)] 2, 8, 18, 32,…… ⇒ 50 [∵ 2,(2+6),(8+6+4),(18+6+4+4), (32+6+4+4+4)] 2, 4, 8, 14, 22, 32…. ⇒44 [∵ 2,(2+2),(4+2+2),(8+2+2+2), (14+2+2+2+2)] 0, 5, 12, 21, 32….. ⇒ 45 [∵ 0,(0+5),(5+5+2),(12+5+2+2), (21+5+2+2+2)] 13, 17, 25, 41,….. ⇒ 73 [∵ 13,(13+22 ),(17+23 ),(25+24 ), (41+25 )] 5, 7, 11, 19,….. ⇒ 5 [∵ 5,(5+21)(7+22 ),(11+23 ),(19+24 )] 8 … ⇒ [∵ 4,(4+21)(6+22 ),(10+23 ),(18+24 )] 3, 6, 4, 9, 5, 12, 6,…. ⇒ 5 ,∵ t1:t3:t5:t7 ⇒ 5 | t2:t4:t6:t8 ⇒ 9 5- 8 9 … ⇒ 7 ,∵ (t1 +4),(t2+8)(t3+4)(t4+8)] 7 5 5 8 …… ⇒ 9 ,∵ t3:t5:t7 ⇒ ( 7-2),(27-4),(27-6),(27-8)| t4:t6:t8 ⇒ (5 ) (5 ) (5 9)-
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http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com 0, 9, 17, 24…35, 39, 42 ….⇒ 5 8 … ⇒ 1, 3, 6 9 5 … ⇒ 8 7 … ⇒ 7 5 … ⇒ 7 9 … 5 ⇒ … 9 ⇒ 7 8 5 5 9…… ⇒ 7 … ⇒ 7 5 9 7 … ⇒ 5 15, 13, 12, 11, 9, 9.. ⇒ 7 8 8 ⇒ 7 8 5 8 … ⇒ 9 9 7 5 8 … ⇒ 9 5 7 … ⇒ 99 5 ⇒ 7 5 7 … ⇒ 7 5 8 7 … ⇒ 8 9 7 … 5 5 ⇒ 8 21, 18, 9 7 … ⇒ 8 5 5 9 … ⇒ 5 … ⇒ 9 7 7 5 ⇒ 5 5 9 5 …⇒ 5 5 … ⇒ 7 7 8 8 8 … ⇒ 8 3, 7, 28, 32, 8, 12, 48, … ⇒5
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