1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# If a + b + c = 2s, then prove the following identities (a) s2 + (s âˆ’ a)2 + (s âˆ’ b)2 + (s âˆ’ c)2 = a2 + b2 + c2 (b) a2 + b2 âˆ’ c2 + 2ab = 4s (s âˆ’ c) (c) c2 + a2 âˆ’ b2 + 2ca = 4s (s âˆ’ b) (d) a2 âˆ’ b2 âˆ’ c2 + 2ab = 4(s âˆ’ b) (s âˆ’ c) (e) (2bc + a2 âˆ’ b2 âˆ’ c2) (2bc âˆ’ a2 + b2 + c2) = 16s (s âˆ’ a) (s âˆ’ b) (s âˆ’ c) (f)

Open in App
Solution

## It is given that a + b + c = 2s (a) We need to show that Consider the left hand side. Hence, . (b) We need to show that Consider the left hand side. Hence, (c) We need to show that Consider the left hand side. Hence, (d) We need to show that Consider the left hand side. Using, a + b + c = 2s, we get Hence, (e) We need to show that Consider the left hand side. Using a + b + c = 2s, we get: Hence, (f) We need to show that Consider the left hand side. Using, a + b + c = 2s, we get Hence,

Suggest Corrections
3
Join BYJU'S Learning Program
Related Videos
Algebraic Identities
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program