题目内容
3.阅读材料:对于任何数,我们规定符号$|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|$的意义是$|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|$=ad-bc.例如:$|\begin{array}{l}{1}&{2}\\{3}&{4}\end{array}|$=1×4-2×3=-2.
(1)按照这个规定,请你计算$|\begin{array}{l}{1}&{-2}\\{3}&{-1}\end{array}|$|的值;
(2)按照这个规定,请你计算 (x-2)2+(y+$\frac{1}{5}$)2=0时,$|\begin{array}{l}{-3{x}^{2}+y}&{{x}^{2}+y}\\{3}&{-2}\end{array}|$值.
分析 (1)根据题意可知列出式子求解.
(2)先化简所求的式子,然后将x与y的值代入即可求出答案.
解答 解:(1)由题意可知:$|\begin{array}{l}{1}&{-2}\\{3}&{-1}\end{array}|$=1×(-1)-(-2)×3=-1+6=5;
(2)∵(x-2)2+(y+$\frac{1}{5}$)2=0,
∴x=2,y=-$\frac{1}{5}$,
∴$|\begin{array}{l}{-3{x}^{2}+y}&{{x}^{2}+y}\\{3}&{-2}\end{array}|$=-2(-3x2+y)-3(x2+y)
=6x2-2y-3x2-3y
=3x2-5y
=3×4-5×(-$\frac{1}{5}$)
=12+1
=13
点评 本题考查新定义型运算,涉及整式的加减,有理数混合运算的,题目较为综合.
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