plzzz ans....Thnk u....Second part
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I think there is some mistake in the sum.
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since , a , b, c , d are in continued proportion
=> a : b :: b : c :: c : d
=> a / b = b / c = c / d
=> a / b = b / c
=> b² = ac
=> b / c = c / d
=> c² = bd
ad = bc ( since , a , b, c , d are in geometric progression)
=> LHS = (a²-b²)(c²-d²)
=> (a²-ac)(bd-d²)
=> a (a-c) d (b-d)
=> ad (a-c)(b-d)
=> bc (a-c)(b-d)
=> c ( a-c ) b ( b-d )
=> (ac-c²)(b²-bd)
=> (b²-c²)(b²-c²)
=> (b²-c²)²
RHS = (b²-c²)²
since , LHS = RHS
proved
=> a : b :: b : c :: c : d
=> a / b = b / c = c / d
=> a / b = b / c
=> b² = ac
=> b / c = c / d
=> c² = bd
ad = bc ( since , a , b, c , d are in geometric progression)
=> LHS = (a²-b²)(c²-d²)
=> (a²-ac)(bd-d²)
=> a (a-c) d (b-d)
=> ad (a-c)(b-d)
=> bc (a-c)(b-d)
=> c ( a-c ) b ( b-d )
=> (ac-c²)(b²-bd)
=> (b²-c²)(b²-c²)
=> (b²-c²)²
RHS = (b²-c²)²
since , LHS = RHS
proved
Radhika411:
In this how ad=bc????
in fifth step
a , b, c ,d are in continued proportion
a/b = b/c = c/d
a/b = c/d => ad = bc
i meant => a/b = c/d
ad = bc (cross multiply)
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