Toán Lớp 7: 3)Cho a/b=c/d. Chứng minh a) ac/bd=a^2+c^2/b^2+d^2 b) 2a^2-b^2/2c^2-d^2=ac/bd 4) Cho a^2=b.c Chứng minh: a+b/a-c=c+a/c-a

Question

Toán Lớp 7:  3)Cho a/b=c/d. Chứng minh a) ac/bd=a^2+c^2/b^2+d^2 b) 2a^2-b^2/2c^2-d^2=ac/bd 4) Cho a^2=b.c Chứng minh: a+b/a-c=c+a/c-a

truongthanhhung · Answer

a]Ta c&oacute; :              a      b         =         c      d         =    k     ab=cd=k            &rarr;    a    =    b    k    ;    c    =    d    k     &rarr;a=bk;c=dk      Ta lại c&oacute; :               a    c        b    d          =          b    k    .    d    k        b    d          =           (     b    d     )     .      k      2          b    d          =      k      2       acbd=bk.dkbd=(bd).k2bd=k2                    a      2      +      c      2            b      2      +      d      2            =             (     b    k     )       2      +       (     d    k     )       2            b      2      +      d      2            =            b      2      .      k      2      +      d      2      .      k      2            b      2      +      d      2            =           (       b      2      +      d      2       )     .      k      2            b      2      +      d      2            =      k      2       a2+c2b2+d2=(bk)2+(dk)2b2+d2=b2.k2+d2.k2b2+d2=(b2+d2).k2b2+d2=k2            &rArr;          a    c        b    d          =            b      2      +      c      2            d      2      +      d      2             &rArr;acbd=b2+c2d2+d2   ( đpcm )   b]V&igrave;           a      b         =         c      d          ab=cd          &rArr;          a    c        b    d          =           c      2          d      2           (    1    )     &rArr;acbd=c2d2(1)   (Nh&acirc;n cả 2 vế với           c      d         )     cd)     V&igrave;           a      b         =         c      d          ab=cd          &rArr;           a      2          b      2           =          a    c        b    d          (    2    )     &rArr;a2b2=acbd(2)  (Nh&acirc;n cả 2 vế với           a      b          ab     Từ      1    ,    2    &rArr;          a    c        b    d          =           a      2          b      2           =           c      2          d      2           =            a      2      +      c      2            b      2      +      d      2             1,2&rArr;acbd=a2b2=c2d2=a2+c2b2+d2     Vậy đpcm   4)Do         a      2      =    b    c    &rArr;       a      b       =       c      a        a2=bc&rArr;ab=ca      Đặt          a      b       =       c      a       =    k    &rArr;     {         a    =    b    .    k          c    =    a    .    k             ab=ca=k&rArr;{a=b.kc=a.k      Ta c&oacute;:             a    +    b        a    &minus;    b        =        b    .    k    +    b        b    .    k    &minus;    b        =        b    .     (     k    +    1     )         b    .     (     k    &minus;    1     )         =        k    +    1        k    &minus;    1         (    1    )      a+ba&minus;b=b.k+bb.k&minus;b=b.(k+1)b.(k&minus;1)=k+1k&minus;1(1)                c    +    a        c    &minus;    a        =        a    .    k    +    a        a    .    k    &minus;    a        =        a    .     (     k    +    1     )         a    .     (     k    &minus;    1     )         =        k    +    1        k    &minus;    1         (    2    )      c+ac&minus;a=a.k+aa.k&minus;a=a.(k+1)a.(k&minus;1)=k+1k&minus;1(2)      Từ (1) v&agrave; (2)       &rArr;        a    +    b        a    &minus;    b        =        c    +    a        c    &minus;    a         (        đ       p    c    m     )                   cho mik c&acirc;u tl hay nhất đi !!!