vikasp99 wrote:

If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) ?

(A) 1/6

(B) 25/144

(C) 49/144

(D) 7/12

(E) 73/144

We can start by adding together (1/p^2) + (1/q^2) by first obtaining a common denominator:

(q^2/q^2)(1/p^2) + (p^2/p^2)(1/q^2)

q^2/[(q^2)(p^2)] + p^2/[(q^2)(p^2)]

(q^2 + p^2)/(pq)^2

Since pq =12, we have:

(q^2 + p^2)/(12)^2

(q^2 + p^2)/144

To determine the value of q^2 + p^2, we can do the following:

(p + q)^2 = (7)^2

p^2 + q^2 + 2pq = 49

Since pq = 12, we know:

p^2 + q^2 + 24 = 49

p^2 + q^2 = 25

Thus, (q^2 + p^2)/144 = 25/144

Answer: B

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