Question

( frac{7+sqrt{5}}{7-sqrt{5}}-frac{7-sqrt{5}}{7+sqrt{5}}=a+b sqrt{5} )
( Rightarrow frac{(7+sqrt{5})^{2}-(7-sqrt{5})^{2}}{(7+sqrt{5})(7-sqrt{5})}=a+b sqrt{5} )
( Rightarrow frac{49+5+14 sqrt{5}-49-5+14 sqrt{5}}{49-5}=a+6 sqrt{5} )
( Rightarrow frac{28 sqrt{5}}{44}=a+b sqrt{5} )
( Rightarrow frac{7 sqrt{5}}{11}=a+b sqrt{5} )
Companing coeficients on both sides, ( a=0 )
( b=frac{7}{11} )

# THIS -7-55 7-55 7455 =a+b5 -

Solution