Question

If $\frac{4+\sqrt{5}}{4-\sqrt{5}}-\frac{4-\sqrt{5}}{4+\sqrt{5}}=a+b\sqrt{5}$, find the values of a and b.

• A. $0,\frac{9}{10}$
• B. $0,\frac{7}{10}$
• C. $0,\frac{16}{11}$
• D. $1,\frac{16}{11}$

Answer 1

The correct option is C $0,\frac{16}{11}$

$\frac{4+\sqrt{5}}{4-\sqrt{5}}-\frac{4-\sqrt{5}}{4+\sqrt{5}}$

$\frac{(4+\sqrt{5}{)}^2-(4-\sqrt{5}{)}^2}{11}=\frac{21+8\sqrt{5}-(21-8\sqrt{5})}{11}$

$=\frac{16\sqrt{5}}{11}$

$a=0b=16/11$