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Polynomials

Question

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Evaluate: $fraction numerator square root of 5 plus square root of 2 over denominator square root of 5 minus square root of 2 end fraction comma$ given that $square root of 10 equals 3.162$ .

Solution

fraction numerator square root of 5 plus square root of 2 over denominator square root of 5 minus square root of 2 end fraction space space space space space space space space space

equals space fraction numerator square root of 5 plus square root of 2 over denominator square root of 5 minus square root of 2 end fraction. fraction numerator square root of 5 plus square root of 2 over denominator square root of 5 plus square root of 2 end fraction equals space fraction numerator left parenthesis square root of 5 plus square root of 2 right parenthesis squared over denominator 5 minus 2 end fraction equals space fraction numerator 5 plus 2 plus 2 square root of 5 square root of 2 over denominator 3 end fraction equals space fraction numerator 7 plus 2 square root of 10 over denominator 3 end fraction equals space fraction numerator 7 plus 2 cross times 3.162 over denominator 3 end fraction equals space fraction numerator 13.324 over denominator 3 end fraction equals space 4.441 top enclose 3

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