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maheshwaranlupp0yaxy:
Continued proportion means that are they in AP
??
No
Ratio and proportion
Are u studying in 8th or 9th?
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as , a , b , c are in continued proportion
=> a : b :: b : c
=> a/b = b/c
=> b² = ac
LHS = (pa² + qab + rb²) / (pb² + qbc + rc² )
=> ( pa² + qab + rac ) / ( pac + qbc + rc² ). (as , b² = ac )
=> a ( pa + qb + rc ) / c ( pa + qb + rc )
as , ( pa + qb + rc ) gets cancelled out
=> LHS = a/c
RHS = a/c
since , LHS = RHS
hence , PROVED
hope this helps
=> a : b :: b : c
=> a/b = b/c
=> b² = ac
LHS = (pa² + qab + rb²) / (pb² + qbc + rc² )
=> ( pa² + qab + rac ) / ( pac + qbc + rc² ). (as , b² = ac )
=> a ( pa + qb + rc ) / c ( pa + qb + rc )
as , ( pa + qb + rc ) gets cancelled out
=> LHS = a/c
RHS = a/c
since , LHS = RHS
hence , PROVED
hope this helps
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