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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
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Given that a,b$\xi$ c are in AP,which of the following is true?

$(a)\;(a-c)^2=4b^2-ac\qquad(b)\;(a-b)^2=4c^2-ab\qquad(c)\;(a-c)^2=4(b^2-ac)\qquad(d)\;(b-c)^2=4(a^2-bc)$

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Answer : (c) $ (a-c)^2=4(b^2-ac)$
Explanation : Given a,b,c are in AP
$2b=a+c$
$(a+c)^2=(2b)^2$
$a^2+c^2+2ac=4b^2$
$subtracting\; -4ac \;on both\; sides $
$a^2+c^2+2ac-4ac=4b^2-4ac$
$a^2+c^2-2ac=4b^2-4ac$
$(a-c)^2=4(b^2-ac).$
answered Jan 2, 2014 by yamini.v
 

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