解:a、b互為倒數(shù),a、c互為相反數(shù),
即ab=1,a+c=0.
∵|d|=2,
∴d=±2,d
2=4.
∴d
2-d•(
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)
2=4-d×(
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)
2=4-
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d,
當(dāng)d=2時,原式=4-
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×2=3
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;
當(dāng)d=-2時,原式=4-
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×(-2)=4
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.
分析:根據(jù)倒數(shù),相反數(shù),絕對值的性質(zhì)可知ab=1,a+c=0,d=±2.根據(jù)已知條件代入原式求解.
點(diǎn)評:主要考查倒數(shù),相反數(shù),絕對值的概念和性質(zhì)以及有理數(shù)的混合運(yùn)算.
倒數(shù)的定義:若兩個數(shù)的乘積是1,我們就稱這兩個數(shù)互為倒數(shù).
相反數(shù)的定義:只有符號不同的兩個數(shù)互為相反數(shù),0的相反數(shù)是0;
絕對值規(guī)律總結(jié):一個正數(shù)的絕對值是它本身;一個負(fù)數(shù)的絕對值是它的相反數(shù);0的絕對值是0.