命题:“若a,b,c成等比数列,则b^2=ac”及其逆命题,否命题,逆否命题正确的个数是?

\u547d\u9898\u201c\u82e5a\uff0cb\uff0cc\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u5219b 2 =ac\u201d\uff0c\u5b83\u7684\u9006\u547d\u9898\u3001\u5426\u547d\u9898\u3001\u9006\u5426\u547d\u9898\u4e2d\u6709______\u4e2a\u771f\u547d\u9898

\u82e5a\uff0cb\uff0cc\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u5219b 2 =ac\uff0c\u4e0d\u59a8\u4ee4\u5176\u4e3a\u539f\u547d\u9898\uff0c\u5219\u539f\u547d\u9898\u4e3a\u771f\uff1b\u2235\u539f\u547d\u9898\u4e0e\u9006\u5426\u547d\u9898\u4e3a\u7b49\u4ef7\u547d\u9898\uff0c\u2234\u9006\u5426\u547d\u9898\u4e3a\u771f\u547d\u9898\uff1b\u5176\u9006\u547d\u9898\u4e3a\uff1a\u82e5b 2 =ac\uff0c\u5219a\uff0cb\uff0cc\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u4e3a\u5047\uff0c\u5982a=b=c=0\uff0c\u6ee1\u8db3b 2 =ac\uff0c\u4f460\uff0c0\uff0c0\u4e0d\u80fd\u6784\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u7531\u4e8e\u9006\u547d\u9898\u4e0e\u5426\u547d\u9898\u4e3a\u7b49\u4ef7\u547d\u9898\uff0c\u771f\u5047\u6027\u4e00\u81f4\uff0c\u2234\u5426\u547d\u9898\u4e3a\u5047\u547d\u9898\uff0e\u6545\u7b54\u6848\u4e3a\uff1a1

\u4f60\u5b66\u4e86\u590d\u6570\u6ca1\u6709\uff0c\u8981\u5b66\u4e86\u5728\u590d\u6570\u8303\u56f4\u5185\u539f\u547d\u9898\u5c31\u662f\u9519\u7684\uff0c\u4f46\u8981\u662f\u53ea\u5728\u5b9e\u6570\u8303\u56f4\u5185\u5e94\u8be5\u662f\u5bf9\u7684\u624d\u5bf9\u554a

若,则b^2=ac 正确
他的逆否命题也正确
逆命题 若b^2=ac,则a,b,c成等比数列 不正确 例如 a=0,b=0 c=1
否命题 若a,b,c不成等比数列,则b^2≠ac 不正确 例如 a=0,b=0 c=1
正确的个数是2个

2

原命题和逆否命题是等价命题;
逆命题和否命题是等价命题;
等价也称等效.甲、乙两命题等价就是可以互推,可写成甲<=====>乙.
等价命题的特点是真则同真,假则皆假.

2ge

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