Question

16．對(duì)于實(shí)數(shù)a，b，c，d，規(guī)定一種運(yùn)算$|\begin{array}{l}{a}&\\{c}&h8s3khk\end{array}|$=ad-bc，如$|\begin{array}{l}{1}&{0}\\{2}&{（-2）}\end{array}|$=1×（-2）-0×2=-2，那么當(dāng)$|\begin{array}{l}{2x}&{x}\\{-x}&{x}\end{array}|$=6時(shí)，x的值為$±\sqrt{2}$．

Answer 1

分析 結(jié)合題中所給的運(yùn)算法則，將$|\begin{array}{l}{2x}&{x}\\{-x}&{x}\end{array}|$=6化簡(jiǎn)為2x×x-（-x）×x=6，然后進(jìn)行求解即可．

解答 解：∵$|\begin{array}{l}{2x}&{x}\\{-x}&{x}\end{array}|$=6，
∴2x×x-（-x）×x=6，
∴3x²=6，
∴x=±$\sqrt{2}$．
故答案為：±$\sqrt{2}$．

點(diǎn)評(píng) 本題考查了整式的混合運(yùn)算，解答本題的關(guān)鍵在于熟讀題意，然后結(jié)合題中所給的運(yùn)算法則，將$|\begin{array}{l}{2x}&{x}\\{-x}&{x}\end{array}|$=6化簡(jiǎn)為2x×x-（-x）×x=6，進(jìn)行求解．