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Home » If a, b, c are in AP, and a, x, b and b, y, c are in GP then show that x2, b2, y2are in AP.
If a, b, c are in AP, and a, x, b and b, y, c are in GP then show that x2, b2, y2are in AP.
CBSE | Class 11 | Excercise 12E | Geometrical Progression | Maths | RS Aggarwal
If a, b, c are in AP, and a, x, b and b, y, c are in GP then show that x2, b2, y2are in AP.

Answer : To prove: x2, b2, y2 are in AP.

Given: a, b, c are in AP, and a, x, b an

b, y, c are in GP Proof: As, a,b,c are in AP

⇒ 2b = a + c … (i) As, a,x,b are in GP

⇒ x2 = ab … (ii) As, b,y,c are in GP

⇒ y2= bc … (iii) Considering x2, b2, y2

x2 + y2 = ab + bc [From eqn. (ii) and (iii)]

= b (a + c)

= b(2b) [From eqn. (i)] x2 + y2 = 2b2

From the above equation we can say that x2, b2, y2 are in AP.

i

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