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If `a,b,c` are real numbers such that `3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab+bc+ca)`, than `a,b,c`are inA. AP onlyB. GP onlyC. GP and APD. None of these |
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Answer» Given, `3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab+bc+ca)` `implies 2(a^(2)+b^(2)+c^(2)-ab-bc-ca)+(a^(2)+b^(2)+c^(2)-2a -2b -2c+3)` `implies {(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}+{(a-1)^(2)+(b-1)^(2)+(c-1)}=0` `implies a-b=b-c=c-a=0 " and "a-1=b-1=c-1=0` `implies a=b=c=1` `implies a,b,c` are in GP and AP. Hence, ia the correct answer. |
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