Question

IF P,Q,R ARE IN CONTINUED PROPORTION , PROVE THAT P:R=P^2:Q^2.

Answer 1

Answer:

GIVEN

P,Q, R ARE IN CONTINUED PROPORTION.

THUS

P:Q=Q:R

= P/Q=Q/R.

= Q^2=PR.

NOW

P^2:Q^2=P^2/Q^2= P^2/PR= P/R

= P:R.

SO,

P:R=P^2:Q^2.

Answer 2

Answer:

GIVEN

P,Q, R ARE IN CONTINUED PROPORTION.

THUS

P:Q=Q:R

= P/Q=Q/R.

= Q^2=PR.

NOW

P^2:Q^2=P^2/Q^2= P^2/PR= P/R

= P:R.

SO,

P:R=P^2:Q^2.

hope this helps