Question

State True or False.

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=14\sqrt{5}$

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+7\sqrt{5}b$
$\Rightarrow \frac{{(7+\sqrt{5})}^2-{(7-\sqrt{5})}^2}{(7-\sqrt{5})(7+\sqrt{5})}=a+7\sqrt{5}b$
$\Rightarrow \frac{(54+14\sqrt{5})-(54-14\sqrt{5})}{44}=a+7\sqrt{5}b$
$\Rightarrow \frac{54+14\sqrt{5}-54+14\sqrt{5}}{44}=a+7\sqrt{5}b$
$\Rightarrow 0+\frac{7}{11}\sqrt{5b}=a+7\sqrt{5}b$
Comparing LHS and RHS we get
$\Rightarrow a=0,b=\frac{1}{11}$