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Home » If a, b, c are in AP, x is the GM between a and b; y is the GM between b and c; then show that b2 is the AM between x2 and y2.
If a, b, c are in AP, x is the GM between a and b; y is the GM between b and c; then show that b2 is the AM between x2 and y2.
CBSE | Class 11 | Excercise 12F | Geometrical Progression
If a, b, c are in AP, x is the GM between a and b; y is the GM between b and c; then show that b2 is the AM between x2 and y2.

Answer : To prove: b2 is the AM between x2 and y2.

Given: (i) a, b, c are in AP

  • x is the GM between a and b
  • y is the GM between b and c

Formula used: (i) Arithmetic mean between

(ii) Geometric mean between As a, b, c are in A.P.

⇒ 2b = a + c … (i)

As x is the GM between a and b

⇒ x2 = ab … (ii)

As y is the GM between b and c

⇒ y2 = bc … (iii)

Substituting the value from eqn. (i)= b2
Arithmetic mean of x2 and y2 is Substituting the value from (ii) and (iii)

Hence Proved

 

i

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