Question

If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P2 + 1/Q2?

Answer 1

q=1/p
then rationalize it,you will get a.
write (p2+q2)/(pq)^2

Answer 2

Answer:

$\frac{1}{P^2}+\frac{1}{Q^2} =194$

Step-by-step explanation:

P = 7 + 4√3

PQ = 1

So, $7 + 4 \sqrt{3} \times Q = 1$

So,  $Q = \frac{1}{7 + 4 \sqrt{3}}$

Now we are supposed to find $\frac{1}{P^2}+\frac{1}{Q^2}$

Substitute the values

$\frac{1}{P^2}+\frac{1}{Q^2}$

$\frac{1}{(7 + 4 \sqrt{3})^2}+\frac{1}{( \frac{1}{7 + 4 \sqrt{3}} )^2}$

$194$

Hence  $\frac{1}{P^2}+\frac{1}{Q^2} =194$