if x=2-√3,then find the value of x^2+1/x^2
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Given :
x = 2 + √3
To find :
x² + 1 / x²
Solution ;
x = 2 + √3
⇒ 1 / x = 1 / 2 + √3 × 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.
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