If a=squareroot 2+ 5, then find a +1/a

Answers (1)

Solution:  We have ,

                                  a=sqrt2+5

Then,                       a+frac1a=fraca^2+1a

Rightarrow                                         =frac(sqrt2+5)^2+1sqrt2+5=frac2+25+10sqrt2+1sqrt2+5=frac28+10sqrt25+sqrt2

 Rightarrow                                        frac28+10sqrt25+sqrt2 	imes frac5-sqrt25-sqrt2=frac120+22sqrt223

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