Question

if p=7-4root3 find p^2+1/p^2and p^4+1/p^4​

Answer 1

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

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