Toán Lớp 8: tim gia tri nho nhat cua cac bieu thuc sau x^2+5x+196; (x+1)^2+(3x-4)^2

Question

Toán Lớp 8:  tim gia tri nho nhat  cua cac bieu thuc sau x^2+5x+196; (x+1)^2+(3x-4)^2

landinhngoc97 · Answer

x ^2 +5x+196   = x^2  + 2 . x  . 5/2 + 25/4 + 759/4   = (x+5/2)^2 +759/4  ge 759/4    Dấu = xảy ra :   &hArr; x+5/2 =0 &hArr; x = -5/2   Vậy Min = 759/4 &hArr; x = -5/2   $  $   Ta c&oacute; :   (x+1)^2 +(3x-4)^2   = 10x^2 - 22x +17   Đặt A = 10x^2 - 22x +17   -> 10A = 100x^2 - 220x + 170   -> 10A = (10x)^2 - 2 . 10x . 11 + 121 +49 =  (10x-11)^2 +49  ge 49    Dấu = xảy ra :   &hArr; 10x -11 =0   &hArr; x = 11/10   Vậy để A đạt được Min &hArr; x =11/10

ankim · Answer

x^2+5x+196     =x^2 + 2.x.2,5 + 6,25 + 189,75     =(x + 2,5)^2  + 189,75     (x + 2,5)^2 &ge; 0     &rArr; (x + 2,5)^2  + 189,75 &ge; 0     Hay GTNN = 0 khi   x + 2,5 =0&hArr;x=-2,5     Đặt A=(x+1)^2 + (3x-4)^2     A=x^2 + 2x + 1 + 9x^2 - 24x + 16     A=10x^2 -22x + 17    &rArr; 10A = 100x^2 -220x + 170    =(10x)^2 - 2.10x.11 + 121 + 49     =(10x - 11)^2 + 49     Ta c&oacute;:  (10x - 11)^2 &ge; 0     &rArr; (10x - 11)^2 + 49 &ge; 49     hay 10A &ge; 49     &rArr; A &ge; 4,9     Dấu bằng xảy ra khi 10x -11 =0 &hArr;x=11/10