Given 2p ^ 2-3p-1 = 0, Q ^ 2 + 3q-2 = 0, find the value of (PQ + P + 1) / Q?

Given 2p ^ 2-3p-1 = 0, Q ^ 2 + 3q-2 = 0, find the value of (PQ + P + 1) / Q?

It is known that 2p & # 178; - 3P-1 = 0, Q & # 178; + 3q-2 = 0
So 2p & # 178; - 3P-1 = 0,2 / Q & # 178; - 3 / Q-1 = 0
So p, 1 / Q are two parts of the equation 2x & # 178; - 3x-1 = 0
Then p + 1 / Q = 3 / 2, p * 1 / Q = - 1 / 2
So (PQ + P + 1) / Q = P + 1 / Q + P / Q = 3 / 2-1 / 2 = 1

Given that 7P2 + 3p-2 = 0, 2q2-3q-7 = 0, and PQ ≠ 1, find the value of 1 / P + Q

Observe from the title: q is a solution of the equation 2x2-3x-7 = 0, at the same time, combined with the equation and 7P2 + 3p-2 = 0, we know that 1 / P is also a solution of the equation 2x2-3x-7 = 0, that is to say, Q and 1 / P are two roots of the equation 2x2-3x-7 = 0, according to the relationship between root and coefficient: 1 / P + q = 3 / 2

Given P & # 178; - PQ = 1,4pq-3q & # 178; = 2, find the value of P & # 178; + 3pq-3p & # 178

Analysis
p²+3pq-3q²
=p²-pq+4pq-3q²
=(p²-pq)+(4pq-3q²）
=1+2
=3