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

1.	If a, b, c, d are in GP show thata^2 + b^2 , b^2+c^2, c^2+d^2Are in GP
Answer» Hope it helps?<br>a,b,c,d are in GP ,means :b² = acc² = bd ad = bcFor 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 + 2b²c²Solving 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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