Toán Lớp 8: 1.Tìm Min A=2x^2-x-1 B=3x^2+6x-3 2.Tìm Max A=2x-x^2-4 B=3-2x^2+4x

Question

Toán Lớp 8:  1.Tìm Min A=2x^2-x-1 B=3x^2+6x-3 2.Tìm Max A=2x-x^2-4 B=3-2x^2+4x

thaolanphuobg · Answer

1.   A=2x&sup2;-x-1   =2(x&sup2;-1/2x-1/2)   =2(x&sup2;-1/2x+1/16-9/16)   =2(x&sup2;-1/2x+1/16)-9/8   =2[x&sup2;-2.x. 1/4+(1/4)^2]-9/8   =2(x-1/4)^2-9/8   Ta c&oacute;:(x-1/4)^2&ge;0&forall;x   &rArr;2(x-1/4)^2&ge;0&forall;x   &rArr;2(x-1/4)^2-9/8&ge;-9/8&forall;x   Vậy A_(min)=-9/8 khi x-1/4=0&hArr;x=1/4   B=3x&sup2;+6x-3   =3(x&sup2;+2x-1)   =3(x&sup2;+2x+1-2)   =3(x&sup2;+2x+1)-6   =3(x+1)&sup2;-6   Ta c&oacute;:(x+1)&sup2;&ge;0&forall;x   &rArr;3(x+1)&sup2;&ge;0&forall;x   &rArr;3(x+1)&sup2;-6&ge;-6&forall;x   Vậy B_(min)=-6 khi x+1=0&hArr;x=-1   2.   A=2x-x&sup2;-4   =-(x&sup2;-2x+4)   =-(x&sup2;-2x+1+3)   =-(x&sup2;-2x+1)-3   =-(x-1)&sup2;-3   Ta c&oacute;:(x-1)&sup2;&ge;0&forall;x   &rArr;-(x-1)&sup2;&le;0&forall;x   &rArr;-(x-1)&sup2;-3&le;-3&forall;x   Vậy A_(max)=-3 khi x-1=0&hArr;x=1   B=3-2x&sup2;+4x   =-2(x&sup2;-2x-3/2)   =-2(x&sup2;-2x+1-5/2)   =-2(x&sup2;-2x+1)+5   =-2(x-1)&sup2;+5   Ta c&oacute;:(x-1)&sup2;&ge;0&forall;x   &rArr;2(x-1)&sup2;&ge;0&forall;x   &rArr;-2(x-1)&sup2;&le;0&forall;x   &rArr;-2(x-1)&sup2;+5&le;5&forall;x   Vậy B_(max)=5 khi x-1=0&hArr;x=1