Toán Lớp 9: tìm GTLN a,-2x²+5x-15 c,C=-4x²-4x-7 d,D=-10-8x-16x² e,E=-3x²+12x-13

Question

Toán Lớp 9:  tìm GTLN a,-2x²+5x-15 c,C=-4x²-4x-7 d,D=-10-8x-16x² e,E=-3x²+12x-13

maianhnhiquynh · Answer

a)A=-2x&sup2;+5x-15          =-2(x&sup2;-5/2x+15/2)          =-2(x&sup2;-5/2x+25/16+95/16)          =-2(x&sup2;-5/2x+25/16)-95/8          =-2[x&sup2;-2.x. 5/4+(5/4)^2]-95/8          =-2(x-5/4)^2-95/8   Ta c&oacute;:(x-5/4)^2&ge;0&forall;x   &rArr;2(x-5/4)^2&ge;0&forall;x   &rArr;-2(x-5/4)^2&le;0&forall;x   &rArr;-2(x-5/4)^2-95/8&le;-95/8&forall;x   Vậy A_(max)=-95/8 khi x-5/4=0&hArr;=5/4   c)C=-4x&sup2;-4x-7          =-4(x&sup2;+x+7/4)          =-4(x&sup2;+x+1/4+3/2)          =-4(x&sup2;+x+1/4)-6          =-4[x&sup2;+2.x. 1/2+(1/2)^2]-6          =-4(x+1/2)^2-6   Ta c&oacute;:(x+1/2)^2&ge;0&forall;x   &rArr;4(x+1/2)^2&ge;0&forall;x   &rArr;-4(x+1/2)^2&le;0&forall;x   &rArr;-4(x+1/2)^2-6&le;-6&forall;x   Vậy C_(max)=-6 khi x+1/2=0&hArr;x=-1/2   d)D=-10-8x-16x&sup2;          =-(16x&sup2;+8x+10)          =-(16x&sup2;+8x+1+9)          =-(16x&sup2;+8x+1)-9          =-[(4x)&sup2;+2.4x.1+1&sup2;]-9          =-(4x+1)&sup2;-9   Ta c&oacute;:(4x-1)&sup2;&ge;0&forall;x   &rArr;-(4x-1)&sup2;&le;0&forall;x   &rArr;-(4x-1)&sup2;-9&le;-9&forall;x   Vậy D_(max)=-9 khi 4x-1=0&hArr;x=1/4   e)E=-3x&sup2;+12x-13          =-3(x&sup2;-4x+13/3)          =-3(x&sup2;-4x+4+1/3)          =-3(x&sup2;-4x+4)-1          =-3(x&sup2;-2.x.2+2&sup2;)-1          =-3(x-2)&sup2;-1   Ta c&oacute;:(x-2)&sup2;&ge;0&forall;x   &rArr;3(x-2)&sup2;&ge;0&forall;x   &rArr;-3(x-2)&sup2;&le;0&forall;x   &rArr;-3(x-2)&sup2;-1&le;-1   Ta c&oacute;:(x-2)&sup2;&ge;0&forall;x   &rArr;3(x-2)&sup2;&ge;0&forall;x   &rArr;-3(x-2)&sup2;&le;0&forall;x   &rArr;-3(x-2)&sup2;-1&le;-1&forall;x   Vậy E_(max)=-1 khi x-2=0&hArr;x=2