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    ±³Àç Q&A HOME > ±³Àç > ±³ÀçQ&A

    2017 ÇØÄ¿½º °ø¹«¿ø ±âÃâ+¿¹»ó¹®Á¦Áý ¼öÇÐ | ±³Àç Q&A
    ÀÌ*±â |Á¶È¸ 1619 |2017.09.07 19:16 ÁÖ¼Òº¹»ç [¸µÅ©Çϱâ]

    (1) ±³Àç¸í : 2017 ÇØÄ¿½º °ø¹«¿ø ±âÃâ+¿¹»ó¹®Á¦Áý

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     (√a+√b)²ÀÇ °ªÀ» ±¸Ç϶ó Ç޴µ¥

    À̰ŠǮ¸é lal+lbl+2√abÇØ¼­

    a+b+3=0, ab=1À̹ǷΠa<0,b<0 À̹ǷÎ

    -(a+b)+2√ab=3+2=5 °¡ ³ª¿Í¾ß ÇÏÁö ¾Ê³ª¿ä?


    Ç®ÀÌÁýµµ √ab =-√ab ·Î ³ª¿Ô´Âµ¥ ¸¶À̳ʽº 2°³°¡ ³ª¿Í ºÎÈ£ ¾È¹Ù²î´Â°Ô ¸ÂÁö¾Ê³ª¿ä? 


    ¾È³çÇϼ¼¿ä, ÀÌÀ±±â ´Ô. Çհݵ¿Çà ÇØÄ¿½ºÀÔ´Ï´Ù.

    ÀÌÀ±±â ´ÔÀÇ ¹®ÀÇ»çÇ×À» È®ÀÎÇÏ¿´À¸¸ç, ºü¸¥ ½ÃÀÏ ³»¿¡ ´äº¯µå¸± ¼ö ÀÖµµ·Ï ÇϰڽÀ´Ï´Ù.

    ÇÕ°ÝÇÏ´Â ±×³¯±îÁö ÃÖ°íÀÇ °­ÀÇ¿Í ¼­ºñ½º¸¦ Á¦°øÇÒ ¼ö ÀÖµµ·Ï Ç×»ó ³ë·ÂÇϰڽÀ´Ï´Ù.

    °¨»çÇÕ´Ï´Ù.
    2017/09/07
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    ¾È³çÇϼ¼¿ä, ÀÌÀ±±â ´Ô. Çհݵ¿Çà ÇØÄ¿½ºÀÔ´Ï´Ù.

    2017 ÇØÄ¿½º °ø¹«¿ø ±âÃâ+¿¹»ó¹®Á¦Áý ¼öÇÐ °ü·Ã ÀÌÀ±±â ´ÔÀÇ ¹®ÀÇ»çÇ× È®ÀÎÇÏ¿´½À´Ï´Ù.

    (√a+√b)²À» °è»êÇϸé (√a)²+(√b)²+2√a√bÀÌ µË´Ï´Ù.

    (√a)²+(√b)²=a+b°¡ µÇ´Â ÀÌÀ¯´Â a<0, b<0À̹ǷΠ(√a)²°ú (√b)²Àº À½¼ö°¡ µÇ±â ¶§¹®ÀÔ´Ï´Ù. Áï, (√a)²=a, (√b)²=bÀÔ´Ï´Ù.
    ¿¹¸¦ µé¾î a=-2¶ó°í Çϸé (√a)²=(√-2)²=(√2 i)²=-2ÀÔ´Ï´Ù.
    µû¶ó¼­ (√a)²+(√b)²=a+b°¡ µË´Ï´Ù.
    ·çÆ® ¾ÈÀÇ °ª¿¡ Á¦°öÀ» ÇÏ´Â °æ¿ì Áï, √(a)²À» °è»êÇÒ ¶§´Â ¸»¾¸ÇϽаÍó·³ |a|·Î °è»êÇØ¾ß ÇÕ´Ï´Ù.

    ¹Ý¸é 2√a√b´Â a, b ¸ðµÎ À½¼öÀ̹ǷΠÀ§¿¡¼­ ¼³¸íÇÑ ³»¿ëÀÌ Àû¿ëµÇÁö¸¸ (√a)²°ú ´Ù¸¥ Á¡Àº ab´Â ¾ç¼öÀ̰í a´Â À½¼ö¶ó´Â Á¡ÀÔ´Ï´Ù.
    Áï, µÎ À½¼öÀÇ Á¦°ö±ÙÀ» °öÇÏ¸é ±× °á°ú°ªÀº À½¼ö°¡ ³ª¿À¹Ç·Î °á°ú°ªÀÇ ºÎÈ£´Â -°¡ µÇ°í Á¦°ö±Ù ¾ÈÀÇ À½¼ö³¢¸® °öÇÏ¸é ¾ç¼ö(ab>0)°¡ µÇ¹Ç·Î Á¦°ö±Ù ¾È¿¡´Â µÎ À½¼öÀÇ °öÀ» ±×´ë·Î ³Ö½À´Ï´Ù.(√ab) ±× °á°ú √a√b=-√ab(a<0, b<0)°¡ µË´Ï´Ù.
    ¿¹¸¦ µé¾î a=-2, b=-8À̶ó°í Çϸé
    2√a√b=2√(-2)√(-8)=2(√2)i(√8)i=2i²(√2)(√8)=-2√16=-8
    ·Î °è»êÇÒ ¼ö ÀÖ½À´Ï´Ù.

    µû¶ó¼­ Ç®ÀÌÁý¿¡ Ç®ÀÌÇÑ ´ë·Î (√a+√b)²=a+b-2√ab=-3-2=-5ÀÔ´Ï´Ù.

    ÇÕ°ÝÇÏ´Â ±×³¯±îÁö ÃÖ°íÀÇ °­ÀÇ¿Í ¼­ºñ½º¸¦ Á¦°øÇÒ ¼ö ÀÖµµ·Ï Ç×»ó ³ë·ÂÇϰڽÀ´Ï´Ù.

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