If a, b, c, d are …
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Posted by Jatin Agrawal 5 years, 1 month ago
- 2 answers
Aseem Mahajan 5 years, 1 month ago
b² = ac
c² = bd
ad = bc
For a²+b² , b²+c² , c²+d² in GP , we need to prove :
(b²+c²)² = (a²+b²)(c²+d²)
Solving LHS:
(b²+c²)²= b⁴ + c⁴ + 2b²c²
Solving RHS:
(a²+b²)(c²+d²) = a²c²+a²d²+b²c²+b²d²
= a²c² + b²d² + 2b²c² (because ad=bc)
= (ac)² + (bd)² + 2b²c²
= b⁴ + c⁴ + 2b²c² (because ac = b² , bd = c²)
Hence ,
a²+b² , b²+c² , c²+d² are in GP
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Aseem Mahajan 5 years, 1 month ago
1Thank You