Question

a,b,c are in ap (b+c)2-c2,(c+a)2-b2,(a+b)2-c2 are in ap

Answer 1

a , b , c are in AP then, we have to prove
(b + c)² - a² , (c + a )² - b², (a + b)² - c² are in AP.
means we have to prove ,
(b + c + a)(b+c-a), (b + c + a)(c + a - b), (a + b + c)(a + b - c) are in AP.


now,
a , b , c are in AP.
=> 2a , 2b , 2c are in AP
=> 2a - (a + b + c ) , 2b -(a + b + c ), 2c - (a + b + c) are in AP
=> (a - b - c), (b - c - a), (c - a - b) are in AP
=> -(b + c - a), -(c + a - b) , -(a + b - c) are in AP
=> (b + c - a), (c + a - b), (a + b - c ) are in AP
=> (b + c - a)(b + c + a), (c + a - b)(c + a + b), (a + b - c)(a + b +c ) are in AP
=>(b + c)² - c², (c + a )² - b², (a + b)² - c² are in AP
hence, proved //

Answer 2

best answer in last question i just earn some point....sorry

and use to my hw