Question

If x = 2 - (root)3
Find x2 + 1/x2

Answer 1

Answer:

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x = 2 + √3

⇒1/x = 1/2 + √3 x 2-√3/2-√3

⇒ 1/x = 2√3 / 2²-√3²

⇒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

And, on squaring both sides.

(x + 1/ x)² = (4)²

⇒ x² + 1/ x² + 2 = 16

⇒ x² + 1/ x² = 16 - 2

⇒ x² + 1/ x² = 14.

Hence,

x² + 1/ x² = 14.