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

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

Grade:11

1 Answers

Rohit
11 Points
6 years ago
To prove bc - a^2 + ab - c^2 = 2(ac- b^2)S= bc -a^2 + ab -c^2 S= b(a+c) -(a^2+c^2) Adding and subtracting 2acS=b(a+c) -(a^2+c^2) +2ac -2acS= b(a+c) + 2ac - (a+c)^2 Putting a+c=2b as they are in AP S= b(2b) + 2ac - 4b^2 S= 2( ac - b^2) Hence proved

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