If a and b are rational numbers and `(sqrt(11)-sqrt(7))/(sqrt(11) +sqrt(7))=a - b sqrt(77)`. find the value of a and b.

Explanation

To solve the equation \(\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b\sqrt{77}\), where \(a\) and \(b\) are rational numbers, we will follow these steps:

### Step 1: Rationalize the Denominator
We start with the left-hand side (LHS):
\[ \frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} \]
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator, which is \(\sqrt{11} - \sqrt{7}\):
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