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38 - 3801 2 △ ABC ȹª úß ù À ¹ª*n ∵ 29 = 2 2(2...

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Unformatted text preview: 3801 2 △ ABC ȹª úß ù À ¹ª*n ∵ 29 = 2 2 + (2 + 3) 2 ∴ù Àª* ¹ 2 2 29 9 37 9 52 9 △ ABC B 52 = (1 + 3) 2 + (1 + 2 + 3) 2 37 = 12 + (1 + 2 + 3) 2 2+ 3+¹ ù 1 À ( ª 1 2 B 3 △ABC B 3 3 = 62− 2 × 5 4 × 6 1× 6 − − 2 2 2 = 36 − 5 − 12 − 3 = 16 2 3 1 A 1 C 1 *ª ¹ú ßÈ △ ( 9 28 9 +i Œ7 È È 3È △ È 65 ¹â¼° ½( 99 15 ( Heron B ª ¹ 13 È úß 3802 (1)9 {−10,−9,−8,,−1,1,2,3,,8,9,10}i ΗU á ¹ : + gª* … e Œ 7 i+ (2)( ¹ ù Àª* Œ * 7 ª ˜¡i+ ¹ ú H Ñ À ¹ ú Èߪ* (1)Ȫ* ¹ú ß 9 3 4 5 6 7 8 9 10 11 12 13 14 +i ½( {− n,−(n − 1),−(n − 2),,−1,1,2,3,, (n − 2), (n − 1), n} 9 (-1,-2) (-1,-3) (-1,-4),(-2,-3) (-1,-5),(-2,-4) (-1,-6),(-2,-5),(-3,-4) (-1,-7),(-2,-6),(-3,-5) (-1,-8),(-2,-7),(-3,-6),(-4,-5) (-1,-9),(-2,-8),(-3,-7),(-4,-6) (-1,-10),(-2,-9),(-3,-8),(-4,-7),(-5,-6) (-2,-10),(-3,-9),(-4,-8),(-5,-7) (-3,-10),(-4,-9),(-5,-8),(-6,-7) (-4,-10),(-5,-9),(-6,-8) 9 1 1 2 2 3 3 4 4 5 5 4 3 * ª¶ c } H + iŒ 7 (2) (a)9 n 15 (-5,-10),(-6,-9),(-7,-8) 16 (-6,-10),(-7,-9) 17 (-7,-10),(-8,-9) 18 (-8,-10) 19 (-9,-10) {−10,−9,−8,,−1,1,2,3,: ,g* 8,¶ 9,+s 10} ¡ ¹ ªH c Pi Œ 7 12 × 4 + 2 2 × 4 + 32 × 4 + 4 2 × 4 + 5 2 = 145 n −1 2 3 2 2 1 1 h 4∑ k 2 − ( k =1 n −1 n −1 × ×n n −1 2 ) = 4 × ( 2 2 ) − ( n − 1) 2 2 6 2 = 2n( n − 1)(n + 1) − 3(n − 1) 2 (n − 1)(2n(n + 1) − 3(n − 1)) (n − 1)(2n 2 − n + 3) = = 12 12 12 h n −2 n 2(n − 2)n(n − 1) + 3n × ×( n −1) n n 4∑ k 2 + ( ) 2 = 4 × ( 2 2 ) + ( )2 = 12 2 6 2 k =1 n −1 2 (b)9 n = B * ª H ¶ c }+ À i Œ 7 ˜¡ h @ . [email protected]ƒþˆi+p• • ë @ & @ . E @ƒþˆi+p• • ë @ N * ª H ¶ c }+ À i Œ 7 ¡ ˜ n(2n(n − 2)(n − 1) + 3n) n(2n 2 − 3n + 4) = 12 12 + i … e U* á ª ¹ i : 7 H g 3803 ª¶c}H ÐÐÐÐÐÐÐÐ b B aB eB 10 3 d¦ ↑↑ h→j ↑ i * ª ¶ c È} B b = a + e, f = e + h, j = h + i ∴ c = b + f = a + h + 2e g = f + j = e + i + 2h, d = c + g = a + i + 3e + 3h e = 1, h = 2 ⇒ d = 9 + a + i dB a +i = 3+4 = 4+3B a +i = 3+5 = 5+3B a +i = 4+5 = 5+4 = 3+6 = 6+3B } @7 a→b→c→d ↑↑↑ e→f→g a +i = 4+ 6 = 6+ 4 = 3+ 7 = 7 +3B a + i = [5 + 6 = 6 + 5] B a + i = 4 + 7 = 7 + 4 ⇒ d = 20 3 (a, e, h, i ) = (6,1,3,2) B B @ƒþˆi+pë•Eÿéð` 9 45 ˆ÷C 49 3804 ê•[email protected]ë + i + (1)7 iŒ (2)0( M· * ª ¹Ü Í ˆ ∆ = xyz ( x + y + z ) = 2 s = a + b + c = 2( x + y + z ) a = y + z , b = z + x, c = x + y ∴ xyz = 4( x + y + z ) ⇒ B x A 29 x F z x≥ y≥z y B 11 1 1 3 = ++ ≤ 2 ⇒ z 2 ≤ 12 4 yz zx xy z z = 1 ⇒ xy = 4 x + 4 y + 4 ( x − 4)( y − 4) = 20 = 20 ⋅ 1 = 10 ⋅ 2 = 5 ⋅ 4 ( x, y ) = (24,5), (14,6), (9,8) (a, b, c) = (29,25,6), (20,15,7), (17,10,9) z = 2 ⇒ xy = 2 x + 2 y + 4 ( x − 2)( y − 2) = 8 = 8 ⋅ 1 = 4 ⋅ 2 ( x, y ) = (10,3), (6,4) , (a, b, c) = (13,12,5), (10,8,6) z = 3 ⇒ 3xy = 4 x + 4 y + 12 →←ͪ ˆ¹ Ü * : ª g H¹áUe…i+ * ª ¹ : g HáUe…i+ * ª ¹ ÜÍ ˆ 2.4 D y E z C 3805 A HB 9 B B △ ABC 蹪* H ñ FE B B DF ⁄ ⁄ ACB B GB GE FG = FE FD BC B F E H ¹ª* ñ → η ∵H h hh ∴ ∵ EFC=∠ DFC ⇒ DC CG = FE EG DC CG = FD FG ….(1) B D C G ∵ DF ⁄ ⁄ AC ∴ ………….(2) 9 (1)(2) ⇒ GE FG = FE FD DC CG = FD FG * ª¹ ñ H * ª ¶H äû * ª¹ ñ H 9 DC CG = * ª¹ ñ H FE *ª¹ ñ H EG GE FG = FE FD ð GE GC = FE CD ð ! ...
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