find-values-a-b-c-such-that-1-ax-2-bx-c-1-and-6b-2-8-a-2-3-is-Max-

Question Number 146062 by mnjuly1970 last updated on 10/Jul/21

f i n d v a l u e s a, b, c s u c h t h a t :

- 1 ⩽ a x^{2} + b x + c ⩽ 1

a n d \frac{6 b^{2} + 8 a^{2}}{3} i s M a x \dots

Commented by mr W last updated on 10/Jul/21

{i t}^{'} s n o t p o s s i b l e w i t h a \neq 0 a n d b \neq 0

t h a t - 1 ⩽ a x^{2} + b x + c ⩽ 1 .

t h a t m e a n s, s u c h t h a t

- 1 ⩽ a x^{2} + b x + c ⩽ 1

w e m u s t h a v e a = b = 0 .

- 1 ⩽ c ⩽ 1 .

s i n c e m a x = \frac{6 b^{2} + 8 a^{2}}{3} = 0 \Rightarrow c = 0

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