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If a, b, c, d are in GP show that a^2 + b^2 , b^2+c^2, c^2+d^2 Are in GP

Posted by Jatin Agrawal 4 years, 1 month ago

CBSE > Class 11 > Applied Maths

2 answers

Aseem Mahajan 4 years, 1 month ago

Hope it helps?

1Thank You

Aseem Mahajan 4 years, 1 month ago

a,b,c,d are in GP ,means :
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

1Thank You

ANSWER

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