Question

3．計(jì)算：-3²+6cos45°-$\sqrt{2}$（2-$\sqrt{2}$）+|$\sqrt{2}$-3|．

Answer 1

分析 首先利用特殊角的三角函數(shù)結(jié)合絕對(duì)值的性質(zhì)分別化簡(jiǎn)，進(jìn)而求出答案．

解答 解：-3²+6cos45°-$\sqrt{2}$（2-$\sqrt{2}$）+|$\sqrt{2}$-3|
=-9+6×$\frac{\sqrt{2}}{2}$-2$\sqrt{2}$-2+3-$\sqrt{2}$
=-9+3$\sqrt{2}$-2$\sqrt{2}$+1-$\sqrt{2}$
=-8．

點(diǎn)評(píng) 此題主要考查了二次根式的混合運(yùn)算，正確化簡(jiǎn)各數(shù)是解題關(guān)鍵．