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CBSE Class 10 Answered

if 1/a+b, 1/c+a, 1/a+d are in ap prove that a^2, b^2, c^2 are also in ap  
Asked by sajal2402 | 21 Jan, 2019, 21:10: PM
answered-by-expert Expert Answer
The question is posted wrongly. The correct question is given below
 
if 1/(b+c), 1/(c+a) and 1/(a+b) are in A.P., then prove that a2 , b2 and c2 are also in A.P
-----------------------
 
let us solve the correct one.
 
if 1/(b+c), 1/(c+a) and 1/(a+b) are in A.P., then difference between 2nd term and first term is equal to
difference between 3rd term and 2nd term.
 
hence
begin mathsize 12px style fraction numerator 1 over denominator open parentheses c plus a close parentheses end fraction space minus space fraction numerator 1 over denominator open parentheses b plus c close parentheses end fraction space equals space fraction numerator 1 over denominator open parentheses a plus b close parentheses end fraction minus fraction numerator 1 over denominator open parentheses c plus a close parentheses end fraction fraction numerator b plus c minus c minus a over denominator open parentheses c plus a close parentheses begin display style open parentheses b plus c close parentheses end style end fraction space equals space fraction numerator c plus a minus a minus b over denominator open parentheses a plus b close parentheses begin display style open parentheses c plus a close parentheses end style end fraction space space space space o r space space space space fraction numerator open parentheses b minus a close parentheses over denominator open parentheses c plus a close parentheses begin display style open parentheses b plus c close parentheses end style end fraction space equals space fraction numerator c minus b over denominator open parentheses a plus b close parentheses begin display style open parentheses c plus a close parentheses end style end fraction fraction numerator open parentheses b minus a close parentheses over denominator open parentheses b plus c close parentheses end fraction space equals space fraction numerator open parentheses c minus b close parentheses over denominator open parentheses a plus b close parentheses end fraction space space o r space space space space b squared space minus space a squared space equals space c squared space minus space b squared space space space space space o r space space space space space 2 b squared space equals space a squared space plus space c squared h e n c e space a squared comma space b squared space a n d space c squared space a r e space i n space A. P end style
Answered by Thiyagarajan K | 22 Jan, 2019, 10:35: AM

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