Solution:

Given, ap = bq = cr and b^2 = ac

We need to find the value of q(p + r)/pr

Let's try to simplify the given expressions first:

ap = bq = cr

We can write,

a/b = c/r = p/q = k (let's say)

So, ap = bq = cr = k^2

Now, b^2 = ac

We know, a/b = c/r

So, a/c = b/r = 1/k

b^2 = ac

b^2 = a*c*(1/k^2)

b^2 = k^2*(1/k^2)

b^4 = 1

b = ±1 (since b cannot be 0 as it will make ac = 0, which is not possible)

Now, let's substitute the values of a/b and b^2/ac in q(p+r)/pr

q(p+r)/pr = q/p + q/r

We know, a/b = c/r = p/q

So, p = q(a/b) and r = q(c/b)

Substituting these values in the above expression, we get:

q(p+r)/pr = q/p + q/r

= q/(q*a/b) + q/(q*c/b)

= b/a + b/c

= (bc+ab)/(ac)

= b(a+c)/(ac)

Now, we also know that b^2 = ac

So, a = b^2/c

Substituting this value in the above expression, we get:

q(p+r)/pr = b(a+c)/(ac)

= b(b^2/c + c)/(c*b^2/c)

= (b^3 + bc)/(b^2)

= b + c/b

= ±1 + c/b

We know that b cannot be 0 and we have already proved that b can only be ±1. So, substituting these values, we get:

q(p+r)/pr = ±1 + c/b

= ±1 ± c

= ±1 (since c cannot be 0 as it will make b^2 = ac = 0, which is not possible)

Therefore, the value of q(p+r)/pr is ±1.

Answer: Option 1 or -1.