1
Question
Represent the following mixed infinite decimal periodic fractions as common fractions:
(P3/2+q3/2p−q−p−qP1/2+q1/2)(√pq√p+√qp−q)−1
(P3/2+q3/2p−q−p−qP1/2+q1/2)(√pq√p+√qp−q)−1
Open in App
Solution
(P32+q32p−q−p−qP12+q12)(√pq√p+√qp−q)−1
=((√p+√q)(p−√pq+q)(√p+√q)(√p−√q)−(√p−√q)(√p+√q)(√p+√q))(√pq(√p+√q)(√p+√q)(√p−√q))−1
=(P−√pq+q√p−√q−(√p−√q))(√pq√p−√q)−1
=(P−√pq+q−P−q+2√pq√p−√q)(√p−√q)√pq
=√pq√pq=1
(P32+q32p−q−p−qP12+q12)(√pq√p+√qp−q)−1
=((√p+√q)(p−√pq+q)(√p+√q)(√p−√q)−(√p−√q)(√p+√q)(√p+√q))(√pq(√p+√q)(√p+√q)(√p−√q))−1
=(P−√pq+q√p−√q−(√p−√q))(√pq√p−√q)−1
=(P−√pq+q−P−q+2√pq√p−√q)(√p−√q)√pq
=√pq√pq=1
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
