If a,b,c are in AP then prove that, (bc-a²),(ca-b²),(ab-c²) are in

1.	If a,b,c are in AP then prove that, (bc-a²),(ca-b²),(ab-c²) are in AP.
Answer» Koi na Given: a, b and c ar in APAs we know, if a, b and c are in AP then 2b = a + c------ (1)We have to prove that ( bc - a2\xa0), ( ca - b2\xa0), ( ab - c2\xa0) are in AP.For this we should prove : 2( ca - b2\xa0) = ( bc - a2\xa0)+ ( ab - c2\xa0)Let us consider\xa0( bc - a2\xa0)+ ( ab - c2\xa0)= ab + bc - (a2+c2)= b( a + c ) - [ (a + c)2\xa0- 2ac] [\xa0∵\xa0a2+b2\xa0=\xa0(a + b)2\xa0- 2ab\xa0]= b(2b) - [ ( 2b )2\xa0-2ac] [\xa0∵ From (1) ]= 2b2\xa0- 4b2\xa0+ 2ac= 2ac -\xa02b2= 2(ca - b2) Don\'t know sorry?

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