Question

( a=2+sqrt{3} )
( a^{2}=4+3+4 sqrt{3} )
( Rightarrow a^{2}+frac{1}{a^{2}}=7+4 sqrt{3}+frac{1}{7+4 sqrt{3}} )
( Rightarrow a^{2}+frac{1}{a^{2}}=frac{(1+4 sqrt{3})^{2}+1}{7+4 sqrt{3}} )
( Rightarrow a^{2}+frac{1}{a^{2}}=frac{49+48+56 sqrt{3}+1}{7+4 sqrt{3}} )
( Rightarrow a^{2}+frac{1}{a^{2}}=frac{98+56 sqrt{3}}{7+4 sqrt{3}} )
( Rightarrow a^{2}+frac{1}{a^{2}}=14left(frac{7+43}{7+43}right) )
( Rightarrow a^{2}+frac{1}{a^{2}}=14 )

# If a = 2+5 then find the value of at the

Solution