Question

p = 3-2√2 find value of p^2 +1/p^2​

Answer 1

Answer:

p = 3 - 2√2

Now, to find value of 1/p :

$\sf \frac{1}{p} = \frac{1}{3 - 2 \sqrt{2} } \\ \\ \sf \frac{1}{p} = \frac{1}{3 - 2 \sqrt{2}} \times \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ \\ \sf \frac{1}{p} = \frac{3 + 2 \sqrt{2} }{(3)^{2} - (2 \sqrt{2})^{2} } \\ \\ \sf \frac{1}{p} = \frac{3 + 2 \sqrt{2} }{9 - 8} \\ \\ \sf \frac{1}{p} = 3 + 2 \sqrt{2}$

Again, find ( p + 1/p )

$\sf p + \frac{1}{p} = 3 - \cancel{2 \sqrt{2}} + 3 + \cancel{2 \sqrt{2}} \\ \\ \sf p + \frac{1}{p} = 3 + 3 \\ \\ \sf p + \frac{1}{p} = 6 \\ \\ \bf on \: squaring \: both \: sides : \\ \\ \sf (p + \frac{1}{p})^{2} = (6)^{2} \\ \\ \sf p {}^{2} + \frac{1}{p {}^{2} } + 2 = 36 \\ \\ \sf p {}^{2} + \frac{1}{p {}^{2} } = 36 - 2 \\ \\ \sf p {}^{2} + \frac{1}{p {}^{2} } = 34$

Hence, the answer is 34.

Answer 2

Answer:

ans is 34

Step-by-step explanation:

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