Question

x
$x {}^{2} + \frac{1}{x { \: }^{2} } if \: x = 2 + \sqrt{3}$
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Answer 1

Question : If x = 2 + √3 , find value of x² + 1 / x².

Answer : 14

Step by step explanation :

We know that,

x = 2 + √3

➡️ 1 / x = 1 / 2 + √3 × 2 - √3 / 2 - √3

➡️ 1 / x = 2 - √3 / (2)² - (√3)²

➡️ 1 / x = 2 - √3 / 4 - 3

➡️ 1 / x = 2 - √3

Now,

x + 1 / x = 2 + √3 + 2 - √3

➡️ x + 1 / x = 2 + 2

➡️ x + 1 / x = 4

Now, Squaring both sides.

( x + 1 / x )² = (4)²

➡️ x² + 1 / x² + 2 = 16

➡️ x² + 1 / x² = 16 - 2

➡️ x² + 1 / x² = 14.

Hence,

Final answer :

x² + 1 / x² = 14

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Answer 2

Your answer lies in the attachment !

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