Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Let a, b, be positive real numbers. If a, A 1 , A 2 b are in arithmetic progression, a, G 1 , G 2 , b are in geometric progression and a, H 1 , H 2 , b are in harmonic progression, show that G 1 G= G 2 /H 1 H 2 = A 1 + A 2 / H 1 H 2 = (2a + b) (a + 2b)/ 9ab

Let a, b, be positive real numbers. If a, A1, A2 b are in arithmetic progression, a, G1, G2, b are in geometric progression and a, H1, H2, b are in harmonic progression,
show that G1 G=G2/H1 H2 = A1 + A2/ H1 H2 = (2a + b) (a + 2b)/ 9ab

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
Hello Student,
Please find the answer to your question
Clearly A1 + A2 = a + b
1/H1 + 1/H2 = 1/a + 1/b
⇒ H1 + H2/H1 H2 = a + b/ab = A1 + A2/G1 G2
⇒ G1 G2 / H1 H2 = A1 + A2/H1 + H2
Also 1/H1 = 1/a + 1/3 (1/b – 1/a) ⇒ H1 = 3ab/2b + a
1/H2 = 1/a + 2/3(1/b – 1/a) ⇒ H2 = 3ab/2a + b
⇒ A1 + A2/H1 + H2 = \frac{a+b}{3ab\left ( \frac{1}{2b+a}+\frac{1}{2a+b} \right )}
= \frac{\left ( 2b+a \right )\left ( 2a+b \right )}{9ab}

Thanks
Aditi Chauhan
askIITians Faculty

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free