Consider the following equations, 2p+3q=18 (2p+3q)2=324 4p2+12pq+9q2=324...(1) 4p2+4pq−3q2=36...(2) Subtracting equation 2 from 1, we get 1 - 2 ⇒8pq+12q2=288 ⇒4q(2p+3q)=288 ⇒4q(18)=288 ⇒q=
288
72
By substituting the value of ‘q’ so obtained, we get 2p+3q=18 2p+3(4)=18 2p+12=18 2p=6 p=3 ∴p=3,q=4 Hence the required value of the given expression is 2p+q =2(3)+4 =10