Question

if 7+root5÷7-root 5 - 7-root 5 ÷7+root 5 = a+ b root 5

Answer 1

Here's your answer for the question

Answer 2

Answer:

a=0 and b=$\frac{7}{11}$

Step-by-step explanation:

The given equation  is :

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+b\sqrt{5}$

Solving the LHS of the above equation, we get

$\frac{(7+\sqrt{5}(7+\sqrt{5})-(7-\sqrt{5})(7-\sqrt{5})}{49-5}$

=$\frac{7+5+14\sqrt{5}-7-5+14\sqrt{5}}{44}$

=$\frac{7}{11}\sqrt{5}$

=$0+\frac{7}{11}\sqrt{5}$

Now, comparing with the RHS of the equation, we get

a=0 and b=$\frac{7}{11}$