answer65 - áUЕ N 6501 D øu^º 2 2<90°(2 N 8\I´ª...

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Unformatted text preview: áUЕ+ N 6501 D øu^º 2 2 <90° (2 N 8\I´ª D ABC ¸»ª*Й=F j0 128I´ª* \ 4.52 ) A >90° (2 ) A N K O B D I C O I K D E M C E M θ B θθ (2 ) ) OD ID BC 8I MD OD ^´ ª MN D BC D DD I D IE D BC D ED IK D MN D K D ∵∠ MIB=∠ MAB+∠ ABI=∠ MAC+∠ IBE=∠ MBC+∠ IBE=∠ MBI 2 D MB = MI D ∆MBN È í MB = MD × MN D MK = MI cos ∠IMD 8 I \´* ª 2 2 2 2 2 2 IO = MI + MO − MI × MO × cos ∠IMD = MI 2+122− MK ×12= MB 2+122− MK ×12 = MD × MN +122− MK ×12 = MD ×24+122− MK ×12 2 2 2 2 = 12 − 2×12( MK −MD ) = R − 2×12× DK = 122− 2×12× IE = 122− 2×12×4.5 w ^ 2 ª´I^8 @4 @F #› @ = @ 7 @4 @F #› @ = @ 7 *ª´I^8 12(12 − 2 × 4.5) =6 (2 2 8 ˜I´ª 8 îh»ª*Й=F 2 2 33 h»ª*Й=F î , @›=F$ƒ•+p× = ˜I´ª* >90°″ 72 62 16 h»ª*Й=F î 52 10 h»ª*Й=F î 2m îh» 32 22 1 š[email protected]› *ª»hîP 6502 0³ 9 20 2 ` * ª ´ (¸ > I * ª º Ì * ª )°è ~ ´ ]0 í * ª º Ì * ª ~ ´ °]è 0 í * ª ´ (¸ > I 2 j» • * ª ´> I¸ hî i (1 ≤ i ≤ j ) ª H´ I * ª » hiF ˜îÐ =™ 20 − j ` * ª º* ̪i´ °~è ]0 í jª H´ I i = 1,2, , * j ´ ÷ 2 ª> I * j D 1,2, ,20 j (20 − j )ª Η ´I 19,36,51,64,75,84,91,96,99,100,99,96,91,84,75,64,51,36,ª19 ¸ ´> I i (1 ≤ i ≤ 10) D 20 − i 2 ª´ IH * ª º 1* 0´ °è Ì ~ª ] 0 í îh 2 » h( í 2 @ ,F @[email protected] ' › * ª » h í F 0Ð =™ * ª ´ >¸ I 10 ` ì 100 2 * ª » h )˜Ð îF = ™ 2 j» • hî 20 − j 2 j (20 − j ) 100I H *ª´ 100 2 10 × 10 = 100 ÷ *ª´ > I וF+ ƒ =› p = 17 ` 72 6503 * ª ´ >¸ I 2 2 ª´ IH ∵∴ * ª » j F h0Ð =™ 42 2 ` ì xD 62 xD kD 24k =x x + x2 − x − 2 3 3 (> 2× 3× 42 242 I´ª 2 x (> I´ª* (xD 1) x (xD 1)( xD 2) 2 x(x3 2x22 xD 2) …… 2 >(I´ª 24 2 x(x3 x22 xD 2) 24 k…… x(x3 x22 xD 2) x(x3 2x22 xD 2) x3 24 ∵24 (I >´ ª 2 3 ∴2 3 x D D xD 62 x3 I(´ ª x(x3 x22 xD 2) 24 k x4 x32 x22 2x ≡ 0 (mod 6) x4 x32 x22 2x ≡ 1 x ≡ 1 (mod 6) 2 x4 x32 x22 2x ≡ 4 x ≡ 2 (mod 6) 2 x4 x32 x22 2x ≡ 3 x ≡ 3 (mod 6) 2 x4 x32 x22 2x ≡ 4 x ≡ 4 (mod 6) 2 x4 x32 x22 2x ≡ 1 x ≡ 5 (mod 6) 2 xD 6nD ´nI (> x ≡ 0 (mod 6) 2 ª x4 x32 x22 2xD 1296 n4 216n32 36n22 nD 3nD 1 ´ — ° ∴ x4 x32 x22 2x D 24 2 2 2 2 2 2 xD 62 2 1. >´ ª(I * >´ ª(I * 2. 3. H H 52 F = › p + * ´ ]í è ª 3 @ 42 F = › p + 2 72 F × ƒ ºÌ~° 2 62 2 o 7 52 2 ·× ƒ 2 1 2 3 4 5 1 4 3 4 1 2≡ 4≡ 0≡ 2≡ 4≡ 2 1≡ 5 (mod 6) 2≡ 4 (mod 6) 3 (mod 6) 2 (mod 6) 1 (mod 6) 9n3) 12 n(3nD 1) 12nD 24(54 n4 >´ ª(I * 6(mod 6)2 ª 13 ( ´> I * ª 13 ( ´> I 2 2 >´ ª(I 12 2* ª ´ >( I 24 2 2 6(mod ´ 6)( ª I> 2 ð F =™ ™ = ™ ` „ F = › `F ð F =™ ™ 32 2 p 1 6504 n, k (æj» ” ˆN¶ª* D ” ˆN¶ª* 2 D D k p† 188 3 n < k < n (i)2 251 4 nD k °~ºª*èí]´0 Ì 1 n−k 63 < < (æj» 7 n + k 439 n p† n ˆN¶ª ” k” ˆN¶ª* 3 188 n− n ≤ 2D 4 251 n ≤ 2 ⇒ n ≤ 2008 D 1004 1504 < k < 1506 D 1505 2 (i)2 D n = 2008 D kp D 2008 2 2 ¶ n ˆNª ” 752 4k < < 3D (i)2 2 251 n D 250 4k − 2n < < 1D 251 n D n > 251 D (i)2 D n = 252,253,254 Oª* ¶” 188 125 3 62 1 188 < k < 189 D 189 < k < 189 D 190 < k < 190 D 2 251 251 4 251 2 ¶ ” ˆNª* D n = 255 D ¶ ” ˆNª* D » j ˆíª*Й=F 2 » j í ˆª*Й=F p ¶ ” ˆNª* ¶ ” N ˆª º Ì 7 °ª*èí]´0 ~ 7 p† 42 ¶ n Oª* ” » n `íª*Й=F j n = 255 p† ¶ n Oª* ” 2008 ˆª ¶”N 2552 190 250 1 < k < 191 D 251 4 k = 191 D 6505 * ª ´‘ H x D ª ´ H h’ d = x− c = x− b= x− a+ 1 ax − 1 = a a 1 a ax 2 − x − a = x− = D d ax − 1 ax − 1 1 ax − 1 ax 3 − x 2 − 2ax + 1 = x− 2 = 2 c ax − x − a ax 2 − x − a a, b, c, d 2 a+ 1 1 1 1 = b+ = c + = d + = x2 b c d a xD ax 2 − x − a = x2 ax 3 − x 2 − 2ax + 1 2 ax 4 − a 2 x 3 − x 3 − 2ax 2 + 2a 2 x + 2 x = 0 D x( x 2 − 2)(ax − a 2 − 1) = 0 D ‘ xH´ª x = 0 D x 2 = 2 D ax − a 2 − 1 = 0 D D 1 1 a + = b + = x = 0D b = c η D x = 0D ’H´ª* b c ax − a 2 − 1 = 0 D x=a+ 1 b x=a+ a =bη ’H´ª* x=± 2D x š[email protected] D ‘ xH´ª* š[email protected]› 84 [email protected]›=F( 72 1 a x2 = 2 D D ‡ g»ª*Й=F ...
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