X equals fraction numerator 1 over denominator square root of 5 minus 2 end fraction f i n d space t h e space v a l u e space o f space X squared plus 1 over x squared

Asked by prahladsumi | 15th Jul, 2020, 02:06: PM

Expert Answer:

To find the value of x2 + 1/x2 when x is given
straight x squared plus 1 over straight x squared equals straight x squared plus 1 over straight x squared plus 2 cross times straight x cross times 1 over straight x minus 2 equals open parentheses straight x plus 1 over straight x close parentheses squared minus 2
equals open parentheses fraction numerator 1 over denominator square root of 5 minus 2 end fraction plus fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator square root of 5 minus 2 end fraction end style end fraction close parentheses squared minus 2
equals open parentheses fraction numerator 1 over denominator square root of 5 minus 2 end fraction plus square root of 5 minus 2 close parentheses squared minus 2
equals open parentheses fraction numerator 10 minus 4 square root of 5 over denominator square root of 5 minus 2 end fraction close parentheses squared minus 2
equals fraction numerator 100 plus 80 minus 80 square root of 5 over denominator 5 plus 4 minus 4 square root of 5 end fraction minus 2
equals fraction numerator 180 minus 80 square root of 5 over denominator 9 minus 4 square root of 5 end fraction minus 2
equals fraction numerator 20 open parentheses 9 minus 4 square root of 5 close parentheses over denominator 9 minus 4 square root of 5 end fraction minus 2
equals 20 minus 2
equals 18

Answered by Renu Varma | 16th Jul, 2020, 12:38: PM