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ICSE Class 9 Answered

If root5 + root3/root over 5-root3 = x-y root15, find X, y. (3 marks) 
Asked by Prajvalsaraff | 15 Nov, 2018, 09:23: PM
answered-by-expert Expert Answer
begin mathsize 18px style fraction numerator square root of 5 plus square root of 3 over denominator square root of 5 minus square root of 3 end fraction equals straight x minus straight y square root of 15 LHS equals fraction numerator begin display style open parentheses square root of 5 plus square root of 3 close parentheses open parentheses square root of 5 plus square root of 3 close parentheses end style over denominator begin display style open parentheses square root of 5 minus square root of 3 close parentheses open parentheses square root of 5 plus square root of 3 close parentheses end style end fraction equals fraction numerator begin display style open parentheses square root of 5 plus square root of 3 close parentheses squared end style over denominator begin display style 25 minus 9 end style end fraction equals fraction numerator begin display style 8 plus 2 square root of 15 end style over denominator begin display style 16 end style end fraction equals fraction numerator begin display style 4 plus square root of 15 end style over denominator begin display style 8 end style end fraction equals 4 over 8 plus fraction numerator square root of 15 over denominator 8 end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction minus open parentheses negative fraction numerator begin display style square root of 15 end style over denominator begin display style 8 end style end fraction close parentheses comparing space we space get straight x equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction straight y equals negative fraction numerator begin display style 1 end style over denominator begin display style 8 end style end fraction end style
Answered by Arun | 16 Nov, 2018, 09:27: AM

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