Question Number 96846 by bobhans last updated on 05/Jun/20
Commented by john santu last updated on 05/Jun/20
![[ a^2 x+(2−2a)x^2 +x^4 ]_1 ^2 ≤ 12 ⇔ a^2 +(2−2a).3 + 15 ≤ 12 a^2 −6a+ 21−12 ≤ 0 a^2 −6a + 9 ≤ 0 (a−3)^2 ≤ 0 ; a = 3](https://www.tinkutara.com/question/Q96847.png)
$$\left[\:{a}^{\mathrm{2}} {x}+\left(\mathrm{2}−\mathrm{2}{a}\right){x}^{\mathrm{2}} +{x}^{\mathrm{4}} \:\right]_{\mathrm{1}} ^{\mathrm{2}} \:\leqslant\:\mathrm{12} \\ $$$$\Leftrightarrow\:{a}^{\mathrm{2}} +\left(\mathrm{2}−\mathrm{2}{a}\right).\mathrm{3}\:+\:\mathrm{15}\:\leqslant\:\mathrm{12}\: \\ $$$${a}^{\mathrm{2}} −\mathrm{6}{a}+\:\mathrm{21}−\mathrm{12}\:\leqslant\:\mathrm{0}\: \\ $$$${a}^{\mathrm{2}} −\mathrm{6}{a}\:+\:\mathrm{9}\:\leqslant\:\mathrm{0}\: \\ $$$$\left({a}−\mathrm{3}\right)^{\mathrm{2}} \:\leqslant\:\mathrm{0}\:;\:{a}\:=\:\mathrm{3}\: \\ $$