Toán Lớp 6: Tìm a,b: a) (a;b)=28 và a+b=224 b) (a;b)=18 và a.b=1944

Question

Toán Lớp 6:  Tìm a,b: a) (a;b)=28 và a+b=224 b) (a;b)=18 và a.b=1944

maitrucloan · Answer

V&igrave; ƯCLN(a,b) = 28      &rArr;{a=28kb=28q  &rArr;{a=28kb=28q   ( ƯCLN(k.q)=1 , k > q )   M&agrave; :      a+b=224  a+b=224         &rArr;28k+28q=224  &rArr;28k+28q=224         &rArr;28(k+q)=224&rArr;k+q=224&divide;28=8  &rArr;28(k+q)=224&rArr;k+q=224&divide;28=8      M&agrave; : k > q    +)     &rArr;{k=7q=1&rArr;{a=28.7b=28.1&rArr;{a=196b=28            a&sdot;b=1944&hArr;18m&sdot;18n=1944&hArr;(18&sdot;18)&sdot;(m&sdot;n)=1944&hArr;324&sdot;mn=1944&hArr;mn=6         ƯCLN  ƯCLN      (a,b)=18  (a,b)=18         &rArr;a=18m(m&isin;N⊛)v&agrave; b=18n(n&isin;N⊛)  &rArr;a=18m(m&isin;N⊛)v&agrave; b=18n(n&isin;N⊛)         a&sdot;b=1944&hArr;18m&sdot;18n=1944&hArr;(18&sdot;18)&sdot;(m&sdot;n)=1944&hArr;324&sdot;mn=1944&hArr;mn=6        xin lỗi v&igrave; sao ch&eacute;p ạ

thienthanh · Answer

Giải đáp:   V&igrave; ƯCLN(a,b) = 28         &rArr;     {              a    =    28    k          b    =    28    q              &rArr;{a=28kb=28q   ( ƯCLN(k.q)=1 , k > q )   M&agrave; :         a    +    b    =    224     a+b=224            &rArr;    28    k    +    28    q    =    224     &rArr;28k+28q=224            &rArr;    28     (     k    +    q     )     =    224    &rArr;    k    +    q    =    224    &divide;    28    =    8     &rArr;28(k+q)=224&rArr;k+q=224&divide;28=8      M&agrave; : k > q    +)        &rArr;     {              k    =    7          q    =    1             &rArr;     {              a    =    28.7          b    =    28.1             &rArr;     {              a    =    196          b    =    28                            a    &sdot;    b    =    1944          &hArr;    18    m    &sdot;    18    n    =    1944          &hArr;     (     18    &sdot;    18     )     &sdot;     (     m    &sdot;    n     )     =    1944          &hArr;    324    &sdot;    m    n    =    1944          &hArr;    m    n    =    6                     Ư       C    L    N     ƯCLN          (     a    ,    b     )     =    18     (a,b)=18            &rArr;    a    =    18    m     (     m    &isin;      N        ⊛         )      v  &agrave;        b    =    18    n     (     n    &isin;      N        ⊛         )      &rArr;a=18m(m&isin;N⊛)v&agrave; b=18n(n&isin;N⊛)               a    &sdot;    b    =    1944          &hArr;    18    m    &sdot;    18    n    =    1944          &hArr;     (     18    &sdot;    18     )     &sdot;     (     m    &sdot;    n     )     =    1944          &hArr;    324    &sdot;    m    n    =    1944          &hArr;    m    n    =    6                     ch&uacute;c bạn học tốt cho tui c&acirc;u trả lời hay nhất nha