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Show that (A-B)^2,(A^2+B^2),(A+B)^2 is an AP |
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Answer» To Prove (A-B)2\xa0,A2+B2 and (A+B)2\xa0is in an AP, We need to show that the difference between the terms are equal.Let a1= (A-B)2 a2=A2\xa0+B2 and a3= (A+B)2Now a2-a1\xa0=\xa0A2\xa0+B2\xa0-\xa0(A-B)2\xa0 and a3\xa0- a2\xa0=(A+B)2\xa0- (A2\xa0+ B2) = A2+B2\xa0-(A2\xa0-2AB+B2) =A2+2AB+B2\xa0-A2\xa0- B2 = A2\xa0+B2\xa0- A2\xa0+2AB - B2 = 2AB = 2ABClearly a2-a1\xa0= a3\xa0- a2\xa0= 2ABSo given terms are in AP with common difference d= 2AB 121221112111111111111111111111111 |
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