Q8 of 104 Page 468

If a, b, c are in GP, prove that .

To prove:


Given: a, b, c are in GP


Formula used: When a,b,c are in GP, b2 = ac


a, b, c are in GP,


⇒ b2 = ac … (i)


… (ii)


Taking LHS =


Substituting the value b2 = ac from eqn. (i)


LHS =




Substituting the value b = from eqn. (ii)




Multiplying and dividing with



⇒


⇒ = RHS


Hence Proved


More from this chapter

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6

Three numbers are in AP, and their sum is 21. If the second number is reduced by 1 and the third is increased by 1, we obtain three numbers in GP. Find the numbers.

 7

The sum of three numbers in GP is 56. If 1, 7, 21 be subtracted from them respectively, we obtain the numbers in AP. Find the numbers

 9

If (a – b), (b – c), (c – a) are in GP then prove that (a + b + c)2 = 3(ab + bc + ca).

 10

If a, b, c are in GP, prove that

(i) a(b2 + c2) = c(a2 + b2)


(ii)


(iii) (a + 2b + 2c)(a – 2b + 2c) = a2 + 4c2


(iv)