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Polynomials

Question

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If find the value of $straight x squared plus 1 over straight x squared.$

Solution

straight x squared plus 1 over straight x squared equals open parentheses straight x plus 1 over straight x close parentheses squared minus 2 space space space space space space space space space space space space.... left parenthesis 1 right parenthesis

x =

2 plus square root of 3

1 over straight x equals fraction numerator 1 over denominator 2 plus square root of 3 end fraction

equals fraction numerator 1 over denominator 2 plus square root of 3 end fraction cross times fraction numerator 2 minus square root of 3 over denominator 2 minus square root of 3 end fraction

equals fraction numerator 2 minus square root of 3 over denominator 4 minus 3 end fraction equals 2 minus square root of 3

therefore space space space space straight x plus 1 over straight x equals 4

From (1),

straight x squared plus 1 over straight x equals left parenthesis 4 right parenthesis squared minus 2 equals 14

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Find two rational numbers between 0.1 and 0.2.

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