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Q.

State true or false.


If a2,  b2,  c2 are in A.P., then b+c,  c+a,  a+b are in H.P.


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a

True

b

False 

answer is A.

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Detailed Solution

Given:
 a2,b2,c2 are in Arithmetic progression (A.P.)
Now Add ab+ac+bc to each term,
a2+ab+ac+bc,b2+ba+bc+ac,c2+ca+cb+ab Taking common values, and rearranging the terms to get,
(a+b)(a+c),(b+c)(b+a),(c+a)(c+b)
Now Dividing each term by (a+b)(b+c)(c+a) we get,
1b+c,1c+a,1a+b The harmonic progression (H.P.) is the inverse of the (A.P.)
Thus, b+c,c+a,a+b are in H.P.
So, the given statement is true.
Correct option is 1.
 
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