x=3+√3
find x^2+9/x^2

Asked by aahnik.mohanty | 26th Nov, 2017, 08:35: PM

Expert Answer:

begin mathsize 16px style straight x equals 3 plus square root of 3
rightwards double arrow 3 over straight x equals fraction numerator 3 over denominator 3 plus square root of 3 end fraction cross times fraction numerator 3 minus square root of 3 over denominator 3 minus square root of 3 end fraction equals fraction numerator 9 minus 3 square root of 3 over denominator 9 minus 3 end fraction equals fraction numerator 3 open parentheses 3 minus square root of 3 close parentheses over denominator 6 end fraction equals fraction numerator 3 minus square root of 3 over denominator 2 end fraction
Now comma
open parentheses straight x plus 3 over straight x close parentheses squared equals open square brackets open parentheses 3 plus square root of 3 close parentheses plus open parentheses fraction numerator 3 minus square root of 3 over denominator 2 end fraction close parentheses close square brackets squared
rightwards double arrow straight x squared plus 6 plus 9 over straight x squared equals open square brackets fraction numerator 6 plus 2 square root of 3 plus 3 minus square root of 3 over denominator 2 end fraction close square brackets squared
rightwards double arrow straight x squared plus 9 over straight x squared equals open square brackets fraction numerator 9 plus square root of 3 over denominator 2 end fraction close square brackets squared minus 6
rightwards double arrow straight x squared plus 9 over straight x squared equals open square brackets fraction numerator 81 plus 18 square root of 3 plus 3 over denominator 4 end fraction close square brackets minus 6
rightwards double arrow straight x squared plus 9 over straight x squared equals fraction numerator 84 plus 18 square root of 3 over denominator 4 end fraction minus 6
rightwards double arrow straight x squared plus 9 over straight x squared equals fraction numerator 42 plus 9 square root of 3 over denominator 2 end fraction minus 6
rightwards double arrow straight x squared plus 9 over straight x squared equals fraction numerator 42 plus 9 square root of 3 minus 12 over denominator 2 end fraction
rightwards double arrow straight x squared plus 9 over straight x squared equals fraction numerator 30 plus 9 square root of 3 over denominator 2 end fraction
end style

Answered by Rashmi Khot | 27th Nov, 2017, 04:45: PM