Toán Lớp 8: tìm GTLN a/5-8x=x^2 b/4x-x^2+1

Question

Toán Lớp 8:  tìm GTLN a/5-8x=x^2 b/4x-x^2+1

tongtung · Answer

$ text{a)5-8x-x&sup2;}$   $ text{=-x&sup2;-2.x.4-16+21}$   $ text{=-(x-4)&sup2;+21}$   $ text{(x-4)&sup2; &ge; 0}$   $ text{&rArr;-(x-4)&sup2; &le; 0}$   $ text{&hArr;-(x-4)&sup2;+21 &le; 21}$   $ text{&rArr;Max=21}$   $ text{Dấu bằng xảy ra khi }$   $ text{x-4=0&hArr;x=4}$   $ text{b)4x-x&sup2;+1}$   $ text{=-x&sup2;+4x-4+5}$   $ text{=-(x-2)&sup2;+5}$   $ text{(x-2)&sup2; &ge; 0}$   $ text{&hArr;-(x-2)&sup2; &le; 0}$   $ text{&hArr; -(x-2)&sup2;+5 &le; 5}$   $ text{&rArr;Max=5}$   $ text{Dấu bằng xảy ra khi x-2=0&hArr;x=2}$

lanminhngoc · Answer

Giải đáp:       Lời giải và giải thích chi tiết:    a) 5-8x-x^2   =-(x^2+8x-5)   =-(x^2+8x+16-21)   =-[(x+4)^2-21]   =-(x+4)^2+21   Ta c&oacute;: (x+4)^2 &ge; 0 &forall;x   &rArr; -(x+4)^2  le 0 &forall;x   &rArr; -(x+4)^2+21  le 21   Vậy y_{max}=21 khi x+4=0&hArr;x=-4   b) 4x-x^2+1   =-(x^2-4x-1)   =-(x^2-4x+4-5)   =-[(x-2)^2-5]   =-(x-2)^2+5   Ta c&oacute;: (x-2)^2 &ge; 0 &forall;x   &rArr; -(x-2)^2  le 0 &forall;x   &rArr; -(x-2)^2+5  le 5   Vậy y_{max}=5 khi x-2=0&hArr;x=2