Question

If 2 + m, 4 + m, 7 + m, are in H.P., find m.​

Answer 1

Answer:

-2/7 , m , 7/2(m+2)  in   G.P

⇒ If a , b ,and c in G.P. ⇒ ac = b²

Therefore,    -2/7 x 7/2 (m+2) = m²  ⇒  m² = -m-2 ⇒ m² + m+2 = 0

⇒ From Shridharcharya rule :  m = -1 +- √(1)² - 8   / 2  = -1-+√7i/2

In case   :  2/7 , m , 7/2(m+2) in G.P. 

⇒ 2/7 x  7/2(m+2) = m²

⇒m² = m+2 ⇒ m²  - m - 2 = 0 ⇒ m²-2m +m -2 = 0

⇒ (m-2)(m+1) = 0 ⇒  m = -1 , 2

So answer depends upon your question.