What is answer of no 4

Asked by sujisbp | 17th May, 2020, 04:22: PM

Expert Answer:

If a=(3+root5)/2, then find the value of a2+1/a2.
Solution:
G i v e n colon space a equals fraction numerator 3 plus square root of 5 over denominator 2 end fraction
a plus 1 over a equals fraction numerator 3 plus square root of 5 over denominator 2 end fraction plus fraction numerator 2 over denominator 3 plus square root of 5 end fraction equals fraction numerator 9 plus 5 plus 6 square root of 5 over denominator 2 open parentheses 3 plus square root of 5 close parentheses end fraction equals fraction numerator 14 plus 6 square root of 5 over denominator 2 open parentheses 3 plus square root of 5 close parentheses end fraction equals fraction numerator 7 plus 3 square root of 5 over denominator 3 plus square root of 5 end fraction
rightwards double arrow open parentheses a plus 1 over a close parentheses squared equals open parentheses fraction numerator 7 plus 3 square root of 5 over denominator 3 plus square root of 5 end fraction close parentheses squared
rightwards double arrow a squared plus 1 over a squared plus 2 cross times a cross times 1 over a equals fraction numerator 49 plus 45 plus 42 square root of 5 over denominator 9 plus 5 plus 6 square root of 5 end fraction equals fraction numerator 94 plus 42 square root of 5 over denominator 14 plus 6 square root of 5 end fraction equals fraction numerator 47 plus 21 square root of 5 over denominator 7 plus 3 square root of 5 end fraction
rightwards double arrow a squared plus 1 over a squared equals fraction numerator 47 plus 21 square root of 5 over denominator 7 plus 3 square root of 5 end fraction minus 2 equals fraction numerator 47 plus 21 square root of 5 minus 14 minus 6 square root of 5 over denominator 7 plus 3 square root of 5 end fraction equals fraction numerator 33 plus 15 square root of 5 over denominator 7 plus 3 square root of 5 end fraction

Answered by Renu Varma | 17th May, 2020, 08:55: PM