If p-3-2 -2- then p 2-1-p2-A- 34B- 35C- 36D- 38

The correct option is A 34 p = 3 2 √(2) ∴ 1/p = 1/3 2 √(2)×3 + 2 √(2)/3 + 2 √(2) = 3 + 2 √(2)/(3)^2 (2 √(2))^2 = 3 + 2 √(2)/9 8 = 3 +2 √(2) p + 1/p = 3 ...

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Byju's Answer

Standard IX

Mathematics

Multiplication and Division of Surds

If p=3-2 √2, ...

Question

If $p = 3 - 2 \sqrt{2}$ , then $p^{2} + \frac{1}{p^{2}} =$ ______.

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Solution

The correct option is A
34

$p = 3 - 2 \sqrt{2}$

$∴ \frac{1}{p} = \frac{1}{3 - 2 \sqrt{2}} \times \frac{3 + 2 \sqrt{2}}{3 + 2 \sqrt{2}}$

$= \frac{3 + 2 \sqrt{2}}{(3)^{2} - (2 \sqrt{2})^{2}}$

$= \frac{3 + 2 \sqrt{2}}{9 - 8}$

$= 3 + 2 \sqrt{2}$

$p + \frac{1}{p} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2}$

= 6

We know ${(p + \frac{1}{p})}^{2} = p^{2} + \frac{1}{p^{2}}$ + 2

$p^{2}$ + $\frac{1}{p^{2}}$ = $(p + \frac{1}{p})^{2}$ - 2

$= (6)^{2} - 2$

= 36 - 2

= 34

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If p=3−2√2, then p2+1p2= ______.

The correct option is A 34 p=3−2√2 ∴ 1p=13−2√2×3+2√23+2√2 =3+2√2(3)2−(2√2)2 =3+2√29−8 =3+2√2 p+1p=3−2√2+3+2√2 = 6 We know (p+1p)2=p2+1p2 + 2 p2 + 1p2 = (p+1p)2- 2 =(6)2−2 = 36 - 2 = 34

If $p = 3 - 2 \sqrt{2}$ , then $p^{2} + \frac{1}{p^{2}} =$ ______.