2011 Λύσεις Σχ. β&I

2 7 7 4 2 3 7 4 2 3 7 4 2 3 7 4 2 4 7 7 2 16 7 9 2 16

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= 2 7 + 7 + 4 2 3 7 – 4 2 = 3 7 + 4 2 3 7 – 4 2 = 4 7 + 7 + 2 16 7 9 2 16 28 + 7 + 32 63 32 = 2 7 2 = –7 2 2 = –14. = 2 2 – 3 2 5 2 + 6 2 – 4 2 = 2 4 2 9 2 25 + 2 36 2 16 8 18 50 + 72 32 x – 5 x + 3 x – 5 + x + 3 = x – 5 2 x + 3 2 2.4. ƒ›˙˜ Ú·ÁÌ·ÙÈÎÒÓ ·ÚÈıÌÒÓ 23
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ii) 2Ô˜ ÙÚfiÔ˜: 8. i) ii) iii) 9. i) ii) ªÂ ·Ó¿Ï˘ÛË ÙÔ˘ 216 Û ÚÒÙÔ˘˜ ·Ú¿ÁÔÓÙ˜ ‚Ú›ÛÎÔ˘Ì 216 = 2 3 Ø 3 3 ÔfiÙ ¤¯Ô˘Ì 10. AÓ ÔÏÏ·Ï·ÛÈ¿ÛÔ˘Ì οı ÎÏ¿ÛÌ· Ì ÙË Û˘˙ËÁ‹ ·Ú¿ÛÙ·ÛË ÙÔ˘ ·- ÚÔÓÔÌ·ÛÙ‹ ÙÔ˘ ¤¯Ô˘ÌÂ: i) ii) iii) = 7 + 6 + 2 42 = 13 + 2 42. 7 + 6 7 6 = 7 + 6 7 + 6 7 – 6 = 7 + 6 2 8 7 5 = 8 7 + 5 7 – 5 = 4 7 + 5 . 4 5 – 3 = 4 5 + 3 5 – 3 5 + 3 = 4 5 + 3 25 – 3 = 4 5 + 3 22 = 10 + 2 3 11 . = 2 3 3 4 2 = 2 2 3 4 = 2 3 2 = 18. 216 75 50 = 2 3 3 3 25 3 2 25 = 5 2 3 3 4 5 2 25 12 75 = 25 4 3 25 3 = 25 2 3 5 3 = 10. = 5 5 = 5 2 5 = 25 5. 5 3 5 3 5 4 6 = 5 3 2 5 1 3 5 4 6 = 5 3 2 + 1 3 + 4 6 = 5 9 6 + 2 6 + 4 6 = 5 15 6 = 5 5 2 = 2 8 9 2 5 6 = 2 8 9 2 5 6 = 2 8 9 + 5 6 = 2 16 18 + 15 18 = 2 31 18 = 2 2 13 18 = 2 2 13 18 . 3 3 4 3 3 = 3 3 4 3 1 3 = 3 3 4 + 1 3 = 3 9 12 + 4 12 = 3 13 12 = 3 3 1 12 = 3 3 12 . = 2 2 2/3 5 = 2 5/3 5 = 2 5/3 1/5 = 2 1/3 = 2 3 . 2 2 2 3 5 = 2 2 2 1/3 5 = 2 2 4/3 5 = 2 2 4/3 1/2 5 ∫∂º∞§∞π√ 2: √𠶃∞°ª∞Δπ∫√π ∞ƒπ£ª√π 24
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11. i) ∞Ó ·Ó·Ï‡ÛÔ˘Ì ÙÔ˘˜ 162 Î·È 98 Û ÁÈÓfiÌÂÓÔ ÚÒÙˆÓ ·Ú·ÁfiÓÙˆÓ ‚Ú›ÛÎÔ˘Ì 162 = 2 Ø 3 4 Î·È 98 = 2 Ø 7 2 ÔfiÙÂ Â›Ó·È ii) ∂›Ó·È 9 12 + 3 20 = 9 12 + (3 2 ) 10 = 9 12 + 9 10 = 9 10 Ø (9 2 + 1) = 82 Ø 9 10 . Î·È 9 11 + 27 6 = 9 11 + (3 Ø 9) 6 = 9 11 + 3 6 Ø 9 6 = 9 11 + (3 2 ) 3 Ø 9 6 = 9 11 + 9 9 = 9 9 (9 2 + 1) = 82 Ø 9 9 ÔfiÙ ¤¯Ô˘Ì μã √ª∞¢∞™ 1. i) ii) 2. i) ∞ÍÈÔÔÈÒÓÙ·˜ ÁÓˆÛÙ¤˜ Ù·˘ÙfiÙËÙ˜ ¤¯Ô˘ÌÂ: ii) ªÂ ÙË ‚Ô‹ıÂÈ· ÙÔ˘ ÂÚˆÙ‹Ì·ÙÔ˜ (i) ·›ÚÓÔ˘Ì 3. i) ∂›Ó·È Ô˘ Â›Ó·È ÚËÙfi˜ ·ÚÈıÌfi˜. = 2 3 + 3 2 + 2 = 4 6 + 9 6 + 12 6 = 25 6 2 3 + 3 3 2 = 2 3 2 + 3 2 2 + 2 2 3 3 2 = 3 + 2 7 3 – 2 7 = 3 + 2 7 2 7 – 3 = 6. = 3 + 2 7 2 3 – 2 7 2 37 + 12 7 37 – 12 7 3 – 2 7 2 = 9 + 4 7 – 12 7 = 37 – 12 7. 3 + 2 7 2 = 9 + 4 7 + 12 7 = 37 + 12 7 Î·È = (· – ‚) (· + ‚) + ·‚ (· – ‚) · – ‚ = · + ‚ + ·‚ . · · · = · · – ‚ · + · · + = · 2 + · ·‚ – ‚ ·‚ – 2 · – ‚ 3 3 2 2 3 2 = 3 3 – 2 2 3 + 2 3 2 3 + 2 = 9 + 3 6 – 2 6 – 4 3 – 2 = 5 + 6. 9 12 + 3 20 9 11 + 27 6 = 82 9 10 82 9 9 = 9 = 3. 162 + 98 50 32 = 2 3 4 + 2 7 2 2 25 2 16 = 9 2 + 7 2 5 2 – 4 2 = 16 2 2 = 16. 2.4. ƒ›˙˜ Ú·ÁÌ·ÙÈÎÒÓ ·ÚÈıÌÒÓ 25
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ii) ∂›Ó·È Ô˘ Â›Ó·È ÚËÙfi˜ ·ÚÈıÌfi˜.
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