According to question,arP−1=64 ..... (i)arQ−1=27 ..... (ii)arR−1=36 ..... (iii)
Dividing Eq. (i) by Eq. (ii), we get
rP−Q=(43)3 ..... (iv)
Dividing Eq. (ii) by Eq. (iii), we get
rQ−R=34
⇒r3Q−3R=(34)3
Multiplying Eq. (iv) and Eq. (v), we get
rP−Q×r3Q−3R=1
⇒rP−Q+3Q−3R=1
⇒rP+2Q−3R=r0
⇒P+2Q−3R=0
⇒P+2Q=3R